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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9A

Question 1

If the mean of 5 observation x, x + 2, x + 4, x + 6 and x  + 8 is 11, find the value of x.

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 2

If
the mean of 25 observations is 27 and each observation is decreased by 7,
what will be the new mean?

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 3

Compute
the mean of the following data:

Class

1-3

3-5

5-7

7-9

Frequency

12

22

27

19

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 4

Find the mean, using direct method:

Class

Frequency

0 – 10

10 – 20

20- 30

30 – 40

40 – 50

50 – 60

7

5

6

12

8

2

Solution 4

We have

Class

FrequencyR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid Value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

0-10

10-20

20-30

30-40

40-50

50-60

7

5

6

12

8

2

5

15

25

35

45

55

35

75

150

420

360

110

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveMean R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 5

Find the mean, using direct method:

Class

Frequency

25 – 35

35 – 45

45 – 55

55 – 65

65 – 75

6

10

8

12

4

 

Solution 5

We have

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Mid – value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

25 – 35

35 – 45

45 – 55

55 – 65

65 – 75

6

10

8

12

4

30

40

50

60

70

180

400

400

720

280

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive Mean, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 6

Find the mean, using direct method:

Class

Frequency

0 – 100

100 – 200

200 – 300

300 – 400

400 – 500

6

9

15

12

8

 

Solution 6

We have

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Mid Value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

0 – 100

100 – 200

200 – 300

300 – 400

400 – 500

6

9

15

12

8

50

150

250

350

450

300

1350

3750

4200

3600

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive Mean, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 7

Using
an appropriate method, find the mean of the following frequency distribution:

Class interval

84-90

90-96

96-102

102-108

108-114

114-120

Frequency

8

10

16

23

12

11

Which
method did you use, and why?

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 8

If
the mean of the following frequency distribution is 24, find the value of p.

Class

0-10

10-20

20-30

30-40

40-50

Frequency

3

4

p

3

2

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 9

The
following distribution shows the daily pocket allowance of children of a
locality. If the mean pocket allowance is Rs.18, find the missing frequency f.

Daily pocket allowance (in )

11-13

13-15

15-17

17-19

19-21

21-23

23-25

Number of children

7

6

9

13

f

5

4

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 10

If
the mean of the following frequency distribution is 54, find the value of p.

Class

0-20

20-40

40-60

60-80

80-100

Frequency

7

p

10

9

13

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 11

The
mean of the following data is 42. Find the missing frequencies x and y if the
sum of frequencies is 100.

Class interval

0-10

10-20

20-30

30-40

40-50

50-60

60-70

70-80

Frequency

7

10

x

13

y

10

14

9

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 12

The
daily expenditure of 100 families are given below.
Calculate f1 and f2 if the mean daily expenditure is Rs.188.

Expenditure (in Rs.)

140-160

160-180

180-200

200-220

220-240

Number of families

5

25

f1

f2

5

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 13

The mean of the following frequency distribution is 57.6 and the sum of the observations is 50.

Class

Frequency

0 – 20

7

20 – 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

40 – 60

12

60 – 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

80 – 100

8

100 – 120

5

Find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogiveand R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive.

Solution 13

We have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid Value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

0 – 20

7

10

70

20 – 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

30

30R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

40 – 60

12

50

600

60 – 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive =18 –
R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

70

1260 – 70R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

80 – 100

8

90

720

100 – 120

5

110

550

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 14

During
a medical check-up, the number of heartbeats per
minute of 30 patients were recorded and summarized as follows:

Number of heart-beats per
minute

65-68

68-71

71-74

74-77

77-80

80-83

83-86

Number of patients

2

4

3

8

7

4

2

Find
the mean heartbeats per minute for these patients, choosing a suitable
method.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 15

Find the mean, using assumed mean method:

Marks

No, of students

0 – 10

10 – 20

20 -30

30 – 40

40 – 50

50 – 60

12

18

27

20

17

6

Solution 15

We have, Let A = 25 be the assumed mean

Marks

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Deviation

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

12

18

27

20

17

6

5

15

25 = A

35

45

55

-20

-10

0

10

20

30

-240

-180

0

200

340

180

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 100

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 300

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence mean = 28

Question 16

Find the mean, using assumed mean method:

Class

Frequency

100 – 120

120 – 140

140 – 160

160 – 180

180 – 200

10

20

30

15

5

Solution 16

Let the assumed mean be 150, h = 20

Marks

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Deviation

di = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive – 150

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive  di

100 – 120

120 – 140

140 – 160

160 – 180

180 – 200

10

20

30

15

5

110

130

150=A

170

190

-40

-20

0

20

40

-400

-400

0

300

200

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 80

 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive di=-300

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Mean = 146.25

Question 17

Find the mean, using assumed mean method:

Class

Frequency

0 – 20

20

20 – 40

35

40 – 60

52

60 – 80

44

80 – 100

38

100 – 120

31

Solution 17

Let A = 50 be the assumed mean, we have

Marks

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Deviation

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

0 – 20

20 – 40

40 – 60

60 – 80

80 – 100

100 – 120

20

35

52

44

38

31

10

30

50 = A

70

90

110

-40

-20

0

20

40

60

-800

-700

0

880

1520

1860

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive= 220

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 18

The
following table gives the literacy rate (in percentage) in 40 cities. Find
the mean literacy rate, choosing a suitable method.

Literacy rate (%)

45-55

55-65

65-75

75-85

85-95

Number of cities

4

11

12

9

4

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 19

Find
the mean of the following frequency distribution using step-deviation method.

Class

0-10

10-20

20-30

30-40

40-50

Frequency

7

10

15

8

10

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 20

Find
the mean of the following data, using step-deviation method:

Class

5-15

15-25

25-35

35-45

45-55

55-65

65-75

Frequency

6

10

16

15

24

8

7

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 21

The
weights of tea in 70 packets are shown in the following table:

Weight (in grams)

200-201

201-202

202-203

203-204

204-205

205-206

Number of packets

13

27

18

10

1

1

Find
the mean weight of packets using step-deviation method.

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 22

Find
the mean of the following frequency distribution using a suitable method:

Class

20-30

30-40

40-50

50-60

60-70

Frequency

25

40

42

33

10

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 23

In
a annual examination marks (out of 90) obtained by students of class X in
mathematics are given below:

Marks obtained

0-15

15-30

30-45

45-60

60-75

75-90

Number of students

2

4

5

20

9

10

Find
the mean marks.

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 24

Find
the arithmetic mean of the following frequency distribution using
step-deviation method:

Age (in year)

18-24

24-30

30-36

36-42

42-48

48-54

Number of workers

6

8

12

8

4

2

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 25

Find the arithmetic mean of each of the following frequency distribution using step-deviation method:

Class

Frequency

500 – 520

520 – 540

540 – 560

560 – 580

580 – 600

600 – 620

14

9

5

4

3

5

Solution 25

Let h = 20 and assume mean = 550, we prepare the table given below:

Age

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

500 – 520

520 – 540

540 – 560

560 – 580

580 – 600

600 – 620

14

9

5

4

3

5

510

530

550 = A

570

590

610

-2

-1

0

1

2

3

-27

-9

0

4

6

15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Thus, A = 550, h = 20, and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 40, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence the mean of the frequency distribution is 544

Question 26

Find the mean age from the following frequency distribution:

Age(in years)

No. of persons

25 – 29

30 – 34

35 – 39

40 – 44

45 – 49

50 – 54

55 – 59

4

14

22

16

6

5

3

Hint: change the given series to the exclusive series

Solution 26

The given series is an inclusive series, making it an exclusive series, we have

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

24.5 – 29.5

29.5 – 34.5

34.5 – 39.5

39.5 – 44.5

44.5 – 49.5

49.5 – 54.5

54.5 – 59.5

4

14

22

16

6

5

3

27

32

37

42 = A

47

52

57

-3

-2

-1

0

1

2

3

-12

-28

-22

0

6

10

9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 70

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Thus, A = 42, h = 5, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 70 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Mean = 39.36 years

Question 27

The following table shows the age distribution of patients of malaria in a village during a particular month:

Age(in years)

No. of cases

5 – 14

15 – 24

24 – 34

35 – 44

45 – 54

55 – 64

6

11

21

23

14

5

Find the average age of the patients.

Solution 27

The given series is an inclusive series making it an exclusive series,we get

class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

4.5 – 14.5

14.5 – 24.5

24.5 – 34.5

34.5 – 44.5

44.5 – 54.5

54.5 – 64.5

6

11

21

23

14

5

9.5

19.5

29.5=A

39.5

49.5

59.5

-2

-1

0

1

2

3

-12

-11

0

23

28

15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Thus, A = 29.5, h = 10, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 80 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Mean = 34.87 years

Question 28

Weight
of 60 eggs were recorded as given below:

Weight (in grams)

75-79

80-84

85-89

90-94

95-99

100-104

105-109

Number of eggs

4

9

13

17

12

3

2

Calculate
their mean weight to the nearest gram.

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 29

The
following table shows the marks scored by 80 students in an examination:

Marks

Less than 5

Less than 10

Less than 15

Less than 20

Less than 25

Less than 30

Less than 35

Less than 40

Number of students

3

10

25

49

65

73

78

80

Calculate
the mean marks correct to 2 decimal places.

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9B

Question 1

In
a hospital, the ages of diabetic patients were recorded as follows. Find the
median age.

Age (in years)

0-15

15-30

30-45

45-60

60-75

Number of patients

5

20

40

50

25

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 2

Compute the median from the following data:

Marks

No. of students

0 – 7

7 – 14

14 – 21

21 – 28

28 – 35

35 – 42

42 – 49

3

4

7

11

0

16

9

 

Solution 2

We prepare the frequency table, given below

Marks

No. of students R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F.

0 – 7

7 – 14

14 – 21

21 – 28

28 – 35

35 – 42

42 – 49

3

4

7

11

0

16

9

3

7

14

25

25

41

50

N = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 50

Now, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency is 25 and corresponding class is 21 – 28.

Thus, the median class is 21 – 28

l = 21, h = 7, f = 11, c = C.F. preceding class 21 – 28 is 14 and  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive= 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Hence the median is 28.

Question 3

The following table shows the daily wages of workers in a factory:

Daily wages

No. of workers

0 – 100

100 – 200

200 – 300

300 – 400

400 – 500

40

32

48

22

8

Find the median daily wage income of the workers.

Solution 3

We prepare the frequency table given below:

Daily wages

Frequency R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F.

0 – 100

100 – 200

200 – 300

300 – 400

400 – 500

40

32

48

22

8

40

72

120

142

150

N = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 150

Now, N = 150, therefore R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 75 is 120 and corresponding class is 200 – 300.

Thus, the median class is 200 – 300

l = 200, h = 100, f = 48

c = C.F. preceding median class = 72 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Hence the median of daily wages is Rs. 206.25.

Hence the median is 28.
Question 4

Calculate the median from the following frequency distribution:

Class

Frequency

5 – 10

10 – 15

15 – 20

20 – 25

25 – 30

30 – 35

35- 40

40 – 45

5

6

15

10

5

4

2

2

 

Solution 4

We prepare the frequency table, given below:

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

C.F

5 – 10

10 – 15

15 – 20

20 – 25

25 – 30

30 – 35

35- 40

40 – 45

5

6

15

10

5

4

2

2

5

11

26

36

41

45

47

49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 49

Now, N = 49 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 24.5 is 26 and corresponding class is 15 – 20.

Thus, the median class is 15 – 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive l = 15, h = 5, f = 15

c = CF preceding median class = 11 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Median of frequency distribution is 19.5

Question 5

Given below is the number of units of electricity consumed in a week in a certain locality:

Consumption

(in units)

No. of consumers

65 – 85

85 – 105

105 – 125

125 – 145

145 – 165

165 – 185

185 – 205

4

5

13

20

14

7

4

Calculate the median.

Solution 5

We prepare the cumulative frequency table as given below:

Consumption

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

C.F

65 – 85

85 – 105

105 – 125

125 – 145

145 – 165

165 – 185

185 – 205

4

5

13

20

14

7

4

4

9

22

42

56

63

67

N = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 67

Now, N = 67 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 33.5 is 42 and the corresponding class 125 – 145.

Thus, the median class is 125 – 145

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive l = 125, h = 20, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive and c = CF preceding the median class = 22, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 33.5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Hence median of electricity consumed is 136.5

Question 6

Calculate the median from the following data:

Height(in cm)

No. of boys

135 – 140

140 – 145

145 – 150

150 – 155

155 – 160

160 – 165

165 – 170

170 – 175

6

10

18

22

20

15

6

3

 

Solution 6

Frequency table is given below:

Height

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

C.F

135 – 140

140 – 145

145 – 150

150 – 155

155 – 160

160 – 165

165 – 170

170 – 175

6

10

18

22

20

15

6

3

6

16

34

56

76

91

97

100

N = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive =100

N = 100, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 50 is 56 and the corresponding class is 150 – 155

Thus, the median class is 150 – 155

l = 150, h = 5, f = 22, c = C.F.preceding median class = 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

Hence, Median = 153.64

Question 7

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

5

25

x

18

7

Solution 7

The frequency table is given below. Let the missing frequency be x.

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive 

C.F

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

5

25

x

18

7

5

30

30 + x

48 + x

55 + x

Median = 24 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive Median class is 20 – 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

l = 20, h = 10, f = x, c = C.F. preceding median class = 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, the missing frequency is 25.

Question 8

The
median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.

Class

0-5

5-10

10-15

15-20

20-25

25-30

30-35

35-40

Frequencies

12

a

12

15

b

6

6

4

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 9

In
the following data the median of the runs scored by 60 top batsmen of the
world in one-day international cricket matches is 5000. Find the missing
frequencies x and y.

Runs scored

2500-3500

3500-4500

4500-5500

5500-6500

6500-7500

7500-8500

Number of batsmen

5

x

y

12

6

2

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 10

If the median of the following frequency distribution is 32.5, find the value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Solution 10

Let R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivebe the frequencies of class intervals 0 – 10 and 40 – 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Median is 32.5 which lies in 30 – 40, so the median class is 30 – 40

l = 30, h = 10, f = 12, N = 40 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 11

Calculate the median for the following data:

Age(in years)

Frequency

19 – 25

26 – 32

33 – 39

40 – 46

47 – 53

54 – 60

35

96

68

102

35

4

Solution 11

The given series is of inclusive form. Converting it into exclusive form and preparing the cumulative frequency table, we get

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F

18.5 – 25.5

25.5 – 32.5

32.5 – 39.5

39.5 – 46.5

46.5 – 53.5

53.5 – 60.5

35

96

68

102

35

4

35

131

199

301

336

340

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivefi = N = 340

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 170 is 199 and the corresponding class is 32.5 – 39.5.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveMedian class is 32.5 – 39.5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivel = 32.5, h = 7, f = 68, c = C.F. of preceding median class = 131

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence median is 36.5 years

Question 12

Find the median wages for the following frequencies distribution:

Wages per day

(in Rs)

Frequency

61 – 70

71 – 80

81 – 90

91 – 100

101 – 110

111 – 120

5

15

20

30

20

8

Solution 12

Given series is in inclusive form converting it into exclusive form and preparing the cumulative frequency table, we get

Wages per day

(in Rs)

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F

60.5 – 70.5

70.5 – 80.5

80.5 – 90.5

90.5 – 100.5

100.5 – 110.5

110.5 – 120.5

5

15

20

30

20

8

5

20

40

70

90

98

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivefi = N =98

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 49 is 70 and corresponding class is 90.5 – 100.5.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivemedian class is 90.5 – 100.5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivel = 90.5, h = 10, f = 30, c = CF preceding median class = 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Median = Rs 93.50

Question 13

Find the median from the following table:

Class

Frequency

1 – 5

6 – 10

11 – 15

16 – 20

21 – 25

26 – 30

31 – 35

35 – 40

40 – 45

7

10

16

32

24

16

11

5

2

Solution 13

The given series is converted from inclusive to exclusive form and preparing the cumulative frequency table, we get

Marks

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F

0.5 – 5.5

5.5 – 10.5

10.5 – 15.5

15.5 – 20.5

20.5 – 25.5

25.5 – 30.5

30.5 – 35.5

35.5 – 40.5

40.5 – 45.5

7

10

16

32

24

16

11

5

2

7

17

33

65

89

105

116

121

123

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivefi = N =123

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 61.5 is 65.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveThe corresponding median class is 15.5 – 20.5.

Then the median class is 15.5 – 20.5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivel = 15.5, h = 5, f = 32, c = C.F. preceding median class = 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Median = 19.95

Question 14

Find the median from the following data:

Marks

No. of students

Below 10

Below 20

Below 30

Below 40

Below 50

Below 60

Below 70

Below 80

12

32

57

80

92

116

164

200

Solution 14

Marks

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

60 – 70

70 – 80

12

20

25

23

12

24

48

36

12

32

57

80

92

116

164

200

N = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The cumulative frequency just greater than 100 is 116 and the corresponding class is 50 – 60.

Thus the median class is 50 – 60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivel = 50, h = 10, f = 24, c = C.F. preceding median class = 92, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive = 100

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Median = 53.33

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9C

Question 1

Find
the mode of the following frequency distribution:

Marks

10-20

20-30

30-40

40-50

50-60

Frequency

12

35

45

25

13

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 2

Compute
the mode of the following data:

Class

0-20

20-40

40-60

60-80

80-100

Frequency

25

16

28

20

5

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 3

Heights
of students of Class X are given in the following frequency distribution:

Height (in cm)

150-155

155-160

160-165

165-170

170-175

Number of students

15

8

20

12

5

Find
the modal height.

Also,
find the mean height. Compare and interpret the two measures of central
tendency.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 4

Find the mode of the following distribution:

Class interval

Frequency

10 – 14

14 – 18

18 – 22

22 – 26

26 – 30

30 – 34

34 – 38

38 – 42

8

6

11

20

25

22

10

4

Solution 4

As the class 26 – 30 has maximum frequency so it is modal class

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, mode = 28.5

Question 5

Given below is the distribution of total household expenditure of 200 manual workers in a city:

Expenditure

No. of manual workers

1000 – 1500

1500 – 2000

2000 – 2500

2500 – 3000

3000 – 3500

3500 – 4000

4000 – 4500

4500 – 5000

24

40

31

28

32

23

17

5

Find the average expenditure done by maximum number of manual workers.

Solution 5

As the class 1500 – 2000 has maximum frequency, so it os modal class

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence the average expenditure done by maximum number of workers = Rs. 1820

Question 6

Calculate the mode from the following data:

Monthly salary

(in Rs)

No. of employees

0 – 5000

5000- 10000

10000 – 15000

15000 – 20000

20000 – 25000

25000 – 30000

90

150

100

80

70

10

Solution 6

As the class 5000 – 10000 has maximum frequency, so it is modal class

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, mode = Rs. 7727.27

Question 7

Compute the mode from the following data:

Age (in years)

No. of patients

0 – 5

5 – 10

10 – 15

15 – 20

20 – 25

25 – 30

30 – 35

6

11

18

24

17

13

5

Solution 7

As the class 15 – 20 has maximum frequency so it is modal class.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence mode = 17.3 years

Question 8

Compute the mode from the following series:

Size

Frequency

45 – 55

55 – 65

65 – 75

75 – 85

85 – 95

95 – 105

105 – 115

7

12

17

30

32

6

10

Solution 8

As the class 85 – 95 has the maximum frequency it is modal class

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, mode = 85.71

Question 9

Compute the mode of the following data:

Class Interval

Frequency

1 – 5

6 – 10

11 – 15

16 – 20

21 – 25

26 – 30

31 – 35

36 – 40

41 – 45

46 – 50

3

8

13

18

28

20

13

8

6

4

Solution 9

The given series is converted from inclusive to exclusive form and on preparing the frequency table, we get

Class

Frequency

0.5 – 5.5

5.5- 10.5

10.5 – 15. 5

15.5 – 20.5

20.5 – 25. 5

25.5 – 30.5

30.5 – 35.5

35.5 – 40.5

40.5 – 45.5

45.5 – 50.5

3

8

13

18

28

20

13

8

6

3

As the class 20.5 – 25.5 has maximum frequency, so it is modal class

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, mode = 23.28

Question 10

The
age wise participation of students in the Annual Function of a school is
shown in the following distribution.

Age (in years)

5-7

7-9

9-11

11-13

13-15

15-17

17-19

Number of students

x

15

18

30

50

48

x

Find
the missing frequencies when the sum of frequencies is 181. Also, find the
mode of the data.

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9D

Question 1

Find the mean, mode and median of the following data:

Class

Frequency

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

60 – 70

5

10

18

30

20

12

5

Solution 1

Let assumed mean be 35, h = 10, now we have

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid-value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

0-10

10-20

20-30

30-40

40-50

50-60

60-70

5

10

18

30

20

12

5

5

15

25

35 = A

45

55

65

-3

-2

-1

0

1

2

3

5

15

33

63

83

95

100

-15

-20

-18

0

20

24

15

N = 100

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(i)Mean R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(ii)N = 100, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Cumulative frequency just after 50 is 63

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveMedian class is 30 – 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivel = 30, h = 10, N = 100, c = 33, f = 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(iii)Mode = 3 × median – 2 × mean

= 3 × 35.67 – 2 × 35.6 = 107.01 – 71.2

= 35.81

Thus, Mean = 35.6, Median = 35.67 and Mode = 35.81

Question 2

Find
the mean, median and mode of the following data:

Class

0-20

20-40

40-60

60-80

80-100

100-120

120-140

Frequency

6

8

10

12

6

5

3

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 3

Find
the mean, median and mode of the following data:

Class

0-50

50-100

100-150

150-200

200-250

250-300

300-350

Frequency

2

3

5

6

5

3

1

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 4

Find
the mode, median and mean for the following data:

Marks obtained

25-35

35-45

45-55

55-65

65-75

75-85

Number of students

7

31

33

17

11

1

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 5

A survey regarding the heights of 50 girls of a class was conducted and the following data was obtained:

Height in cm

No. of girls

120 – 130

130 – 140

140 – 150

150 – 160

160 – 170

2

8

12

20

8

Total

50

Find the mean, Median and mode of the above data.

Solution 5

Let the assumed mean A be 145.Class interval h = 10.

Class

Frequency

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid-Value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F.

120-130

130-140

140-150

150-160

160-170

2

8

12

20

8

125

135

145=A

155

165

-2

-1

0

1

2

-4

-8

0

20

16

2

10

22

42

50

N = 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(i)Mean R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(ii)N = 50, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Cumulative frequency just after 25 is 42

Corresponding median class is 150 – 160

Cumulative frequency before median class, c = 22

Median class frequency f = 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(iii)Mode = 3 median – 2 mean

= 3 151.5 – 2 149.8 = 454.5 – 299.6

= 154.9

Thus, Mean = 149.8, Median = 151.5, Mode = 154.9

Question 6

The following table gives the daily income of 50 workers of a factory:

Daily income(in Rs)

No. of workers

100 – 120

120 – 140

140 – 160

160 – 180

180 – 200

12

14

8

6

10

Find the mean, mode and median of the above data

Solution 6

Class

FrequencyR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid-value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F.

100-120

120-140

140-160

160-180

180-200

12

14

8

6

10

110

130

150= A

170

190

-2

-1

0

1

2

-24

-14

0

6

20

12

26

34

40

50

N = 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

     Let assumed mean A = 150 and h = 20

(i)Mean R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(ii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Cumulative frequency just after 25 is 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveCorresponding frequency median class is 120 – 140

So, l = 120, f = 14, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogiveh = 20, c = 12

                               R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(iii)Mode = 3 Median – 2 Mode

= 3 138.6 – 2 145.2

= 415.8 – 190.4

= 125.4

Hence, Mean = 145.2, Median = 138.6 and Mode = 125.4

Question 7

The table below shows the daily expenditure on food of 30 households in a locality:

Daily expenditure

No. of households

100 – 150

150 – 200

200 – 250

250 – 300

300 – 350

6

7

12

3

2

Find the mean and median daily expenditure on food

Solution 7

Class

FrequencyR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Mid-value

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

C.F.

100-150

150-200

200-250

250-300

300-350

6

7

12

3

2

125

175

225

275

325

-2

-1

0

1

2

-12

-7

0

3

4

6

13

25

28

30

N = 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Let assumed mean = 225 and h = 50

(i)Mean = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

(ii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Cumulative frequency just after 15 is 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivecorresponding class interval is 200 – 250

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And OgiveMedian class is 200 – 250

Cumulative frequency c just before this class = 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence, Mean = 205 and Median = 208.33

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9E

Question 1

Find
the median of the following data by making a ‘less than ogive‘.

Marks

0-10

10-20

20-30

30-40

40-50

50-60

60-70

70-80

80-90

90-100

Number of students

5

3

4

3

3

4

7

9

7

8

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

We plot the points (10, 5), (20, 8), (30, 12), (40, 15), (50, 18),
(60, 22), (70, 29), (80, 38), (90, 45) and (100, 53) to get the ‘less than
type’ ogive as follows:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

At
y = 26.5, affix A.

Through
A, draw a horizontal line meeting the curve at P.

Through
P, a vertical line is drawn which meets OX at M.

OM
= 68 units

Hence,
median marks = 68

Question 2

The
given distribution shows the number of wickets taken by the bowlers in one
-day international cricket matches:

Number of wickets

Less than 15

Less than 30

Less than 45

Less than 60

Less than 75

Less than 90

Less than 105

Less than 120

Number of bowlers

2

5

9

17

39

54

70

80

Draw
a ‘less type’ ogive from the above data. Find the
median.

Solution 2

Number of wickets

Less than 15

Less than 30

Less than 45

Less than 60

Less than 75

Less than 90

Less than 105

Less than 120

Number of bowlers

2

5

9

17

39

54

70

80

We
plot the points (15, 2), (30, 5), (45, 9), (60, 17), (75, 39), (90, 54),
(105, 70) and (120, 80) to get the ‘less than type’ ogive
as follows:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

At y = 40, affix A.

Through
A, draw a horizontal line meeting the curve at P.

Through
P, a vertical line is drawn which meets OX at M.

OM
= 78 units

Hence,
median number of wickets = 78

Question 3

Draw
a ‘more than’ ogive for the data given below which
gives the marks of 100 students.

Marks

0-10

10-20

20-30

30-40

40-50

50-60

60-70

70-80

Number of students

4

6

10

10

25

22

18

5

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

We plot the points (0, 100), (10, 96), (20, 90), (30, 80), (40, 70),
(50, 45), (60, 23) and (70, 5) to get the ‘more than type’ ogive as follows:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

At y = 50, affix A.

Through
A, draw a horizontal line meeting the curve at P.

Through
P, a vertical line is drawn which meets OX at M.

OM
= 47 units

Hence, median marks
= 47

Question 4

The
height of 50 girls of Class X of a school are recorded as follows:

Height (in cm)

135-140

140-145

145-150

150-155

155-160

160-165

Number of girls

5

8

9

12

14

2

Draw
a ‘more than type’ ogive for the above data.

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

We plot the points (135, 50), (140, 45), (145, 37), (150, 28), (155,
16) and (160, 2) to get the ‘more than type’ ogive
as follows:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

At
y = 25, affix A.

Through
A, draw a horizontal line meeting the curve at P.

Through
P, a vertical line is drawn which meets OX at M.

OM
= 151 units

Hence, median
height = 151 cm

Question 5

The
monthly consumption of electricity (in units) of some families of a locality
is given in the following frequency distribution:

Monthly consumption (in units)

140-160

160-180

180-200

200-220

220-240

240-260

260-280

Number of families

3

8

15

40

50

30

10

Prepare
a ‘more than type’ ogive for the given frequency
distribution.

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

We plot the points (140, 156), (160, 153), (180, 145), (200, 130),
(220, 90), (240, 40) and (260, 10) to get the ‘more than type’ ogive as follows:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

At
y = 78, affix A.

Through
A, draw a horizontal line meeting the curve at P.

Through
P, a vertical line is drawn which meets OX at M.

OM
= 226 units

Hence, median
consumption of electricity = 226 units

Question 6

The
following table gives the production yield per hectare of wheat of 100 farms
of a village.

Production yield (kg/ha)

50-55

55-60

60-65

65-70

70-75

75-80

Number of farms

2

8

12

24

38

16

Change
the distribution to a ‘more than type’ distribution and draw its ogive. Using ogive, find the
median of the given data.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

We plot the points (50, 100), (55, 98), (60, 90), (65, 78), (70, 54)
and (75, 16) to get the ‘more than type’ ogive as
follows:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

At
y = 50, affix A.

Through
A, draw a horizontal line meeting the curve at P.

Through
P, a vertical line is drawn which meets OX at M.

OM
= 70.5 units

Hence, median
production yield = 70.5 kg/ha

Question 7

The
table given below shows the weekly expenditures on food of some households in
a locality.

Weekly expenditure (in Rs.)

Number of households

100-200

5

200-300

6

300-400

11

400-500

13

500-600

5

600-700

4

700-800

3

800-900

2

Draw
a ‘less tha type’ and a ‘more than type’ ogive for this distribution.

Solution 7

Less Than Series:

Class interval

Cumulative Frequency

Less than 200

5

Less than 300

11

Less than 400

22

Less than 500

35

Less than 600

40

Less than 700

44

Less than 800

47

Less than 900

49

We
plot the points (200, 5), (300, 11), (400, 22), (500, 35), (600, 40), (700,
44), (800, 47) and (900, 49) to get ‘less than type’ ogive.

More Than Series:

Class interval

Frequency

More than 100

49

More than 200

44

More than 300

38

More than 400

27

More than 500

14

More than 600

9

More than 700

5

More than 800

2

We
plot the points (100, 49), (200, 44), (300, 38), (400, 27), (500, 14), (600,
9), (700, 5) and (800, 2) to get more than ogive.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 8

From the following frequency distribution, prepare the ‘More than Ogive’

Score

No. of candidates

400 – 450

450 – 500

500 – 550

550 – 600

600- 650

650 – 700

700 – 750

750 – 800

20

35

40

32

24

27

18

34

Total

230

Also find the median

Solution 8

More than series

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

 

We plot the points (400, 230), (450, 210), (500, 175), (550, 135), (600, 103), (650, 79), (700, 52), (750, 34)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Hence,R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Take a point A(0, 115) on the y-axis and draw AP||x-axis meeting the curve at P, Draw PM R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogivex-axis intersecting x-axis at M

Then,OM = 590

Hence median = 590

Question 9

The marks obtained by 100 students of a class in an examination are given below:

Marks

No. of students

0 – 5

5 – 10

10 – 15

15 – 20

20 – 25

25 – 30

30 – 35

35 – 40

40 – 45

45 – 50

2

5

6

8

10

25

20

18

4

2

Draw cumulative frequency curves by using (1), less than series and (2) more than series

Hence, find the median

Solution 9

(i) Less than series:

 

Marks

No. of students

Less than 5

Less than 10

Less than 15

Less than 20

Less than 25

Less than 30

Less than 35

Less than 40

Less than 45

Less than 50

2

7

13

21

31

56

76

94

98

100

Plot the points (5, 2), (10, 7), (15, 13), (20, 21), (25, 31), (30, 56), (35, 76), (40, 94), (45, 98) and (50, 100)

                   R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Join these points free hand to get the curve representing “less than” cumulative curve.

(ii)From the given table we may prepare the ‘more than’ series as shown below

Marks

No. of students

More than 45

More than 40

More than 35

More than 30

More than 25

More than 20

More than 15

More than 10

More than 5

More than 0

2

6

24

44

69

79

87

93

98

100

Now, on the same graph paper as above, we plot the point (0, 100), (5, 98), (10, 93), (15, 87), (20, 79), (25, 69), (30, 44), (35, 24) and (40, 6) and (45, 2)

Join these points free hand to get required curve

Here R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Two curves intersect at point P(28, 50)

Hence, the median = 28

Question 10

From the following data, draw the two types of cumulative frequency curves and determine the median:

Height (in cm)

Frequency

140 – 144

144 – 148

148 – 152

152 – 156

156 – 160

160 – 164

164 – 168

168 – 172

172 – 176

176 – 180

3

9

24

31

42

64

75

82

86

34

Solution 10

We may prepare less than series and more than series

(i)Less than series

Height in (cm)

Frequency

Less than 140

Less than 144

Less than 148

Less than 152

Less than 156

Less than 160

Less than 164

Less than 168

Less than 172

Less than 176

Less than 180

0

3

12

36

67

109

173

248

330

416

450

Now on graph paper plot the points (140, 0), (144, 3), (148, 12), (152, 36), (156, 67), (160, 109), (164, 173), (168, 248), (172, 330), (176, 416), (180, 450)

(ii)More than series

Height in cm

C.F.

More than 140

More than 144

More than 148

More than 152

More than 156

More than 160

More than 164

More than 168

More than 172

More than 176

More than 180

450

447

438

414

383

341

277

202

120

34

0

Now on the same graph plot the points (140, 450), (144, 447), (148, 438), (152, 414), (156, 383), (160, 341), (164, 277), (168, 202), (172, 120), (176, 34), (180, 0)

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

The curves intersect at (167, 225).

Hence, 167 is the median.

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9F

Question 1

Write
the median class of the following distribution:

Class

0-10

10-20

20-30

30-40

40-50

50-60

60-70

Frequency

4

4

8

10

12

8

4

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 2

What
is the lower limit of the modal class of the following frequency
distribution?

Age (in years)

0-10

10-20

20-30

30-40

40-50

50-60

Number of patients

16

13

6

11

27

18

Solution 2

Class
having maximum frequency is the modal class.

Here,
maximum frequency = 27

Hence, the modal
class is 40 – 50.

Thus, the lower
limit of the modal class is 40.

Question 3

The
monthly pocket money of 50 students of a class are given in the following
distribution:

Monthly pocket money (in Rs.)

0-50

50-100

100-150

150-200

200-250

250-300

Number of students

2

7

8

30

12

1

Find
the modal class and also give class mark of the modal class.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 4

A
data has 25 observations arranged in a descending order. Which observation
represents the median?

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 5

For
a cetain distribution, mode and median were found
to be 1000 and 1250 respectively. Find mean for this distribution using an
empirical relation.

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 6

In
a class test, 50 students obtained marks as follows:

Marks obtained

0-20

20-40

40-60

60-80

80-100

Number of students

4

6

25

10

5

Find
the modal class and the median class.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 7

Find
the class marks of classes 10-25 and 35-55.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 8

While
calculating the mean of a given data by the assumed-mean method, the following
values were obtained:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Find
the mean.

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 9

The
distributions X and Y with total number of observations 36 and 64, and mean 4
and 3 respectively are combined. What is the mean of the resulting
distribution X + Y?

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 10

In
a frequency distribution table with 12 classes, the class-width is 2.5 and
the lowest class boundary is 8.1, then what is the upper class boundary of
the highest class?

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 11

The
observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in
ascending order. What is the value of x if the median of the data is 63?

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 12

The median of 19
observations is 30. Two more observations are made and the values of these
are 8 and 32. Find the median of the 21 observations taken together.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 14

What
is the cumulative frequency of the modal class of the following distribution?

Class

3-6

6-9

9-12

12-15

15-18

18-21

21-24

Frequency

7

13

10

23

4

21

16

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 15

Find
the mode of the given data:

Class interval

0-20

20-40

40-60

60-80

Frequency

15

6

18

10

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 16

The
following are the ages of 300 patients getting medical treatment in a
hospital on a particular day:

Age (in year)

10-20

20-30

30-40

40-50

50-60

60-70

Number of patients

60

42

55

70

53

20

Form
a ‘less than type’ cumulative frequency distribution.

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 17

In
the following data, find the value of p and q. Also, find the median class
and modal class.

Class

Frequency (f)

Cumulative frequency (cf)

100-200

11

11

200-300

12

p

300-400

10

33

400-500

q

46

500-600

20

66

600-700

14

80

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 18

The
following frequency distribution gives the monthly consumption of electricity
of 64 consumers of a locality.

Monthly consumption (in units)

65-85

85-105

105-125

125-145

145-165

165-185

Number of consumers

4

5

13

20

14

8

Form
a ‘more than type’ cumulative frequency distribution.

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 19

The
following table gives the life-time (in days) of 100 electric bulbs of a
certain brand.

Life-time (in days)

Less than 50

Less than 100

Less than 150

Less than 200

Less than 250

Less than 300

Number of bulbs

7

21

52

79

91

100

From
this table, construct the frequency distribution table.

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 20

The
following table gives the frequency distribution of the percentage of marks
obtained by 2300 students in a competitive examination.

Marks obtained (in percent)

11-20

21-30

31-40

41-50

51-60

61-70

71-80

Number of students

141

221

439

529

495

322

153

(a) Convert the given frequency
distribution into the continuous form.

(b) Find the median class and write
its class mark

(c) Find the modal class and write
its cumulative frequency.

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 21

If
the mean of the following distribution is 27, find the value of p.

Class

0-10

10-20

20-30

30-40

40-50

Frequency

8

p

12

13

10

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Mean Median Mode Of Grouped Data Cumulative Frequency Graph And Ogive

Question 22

Calculate
the missing frequency from the following distribution, it being given that
the median of the distribution is 24.

Age (in years)

0-10

10-20

20-30

30-40

40-50

Number of persons