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NCERT solution class 10 chapter 15 Statistics exercise 15.2 mathematics

EXERCISE 15.2


Page No 275:

Question 1:

The following table shows the ages of the patients admitted in a hospital during a year:

age (in years)

5 − 15

15 − 25

25 − 35

35 − 45

45 − 55

55 − 65

Number of patients

6

11

21

23

14

5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer:

To find the class marks (xi), the following relation is used.

Taking 30 as assumed mean (a), di and fidiare calculated as follows.

Age (in years)

Number of patients

fi

Class mark

xi

di = xi − 30

fidi

5 − 15

6

10

− 20

− 120

15 − 25

11

20

− 10

− 110

25 − 35

21

30

0

0

35 − 45

23

40

10

230

45 − 55

14

50

20

280

55 − 65

5

60

30

150

Total

80

430

From the table, we obtain

Mean of this data is 35.38. It represents that on an average, the age of a patient admitted to hospital was 35.38 years.

It can be observed that the maximum class frequency is 23 belonging to class interval 35 − 45.

Modal class = 35 − 45

Lower limit (l) of modal class = 35

Frequency (f1) of modal class = 23

Class size (h) = 10

Frequency (f0) of class preceding the modal class = 21

Frequency (f2) of class succeeding the modal class = 14

Mode =

Mode is 36.8. It represents that the age of maximum number of patients admitted in hospital was 36.8 years.

Video Solution

Question 2:

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours)

0 − 20

20 − 40

40 − 60

60 − 80

80 − 100

100 − 120

Frequency

10

35

52

61

38

29

Determine the modal lifetimes of the components.

Answer:

From the data given above, it can be observed that the maximum class frequency is 61, belonging to class interval 60 − 80.

Therefore, modal class = 60 − 80

Lower class limit (l) of modal class = 60

Frequency (f1) of modal class = 61

Frequency (f0) of class preceding the modal class = 52

Frequency (f2) of class succeeding the modal class = 38

Class size (h) = 20

Therefore, modal lifetime of electrical components is 65.625 hours.

Video Solution

Question 3:

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

Expenditure (in Rs)

Number of families

1000 − 1500

24

1500 − 2000

40

2000 − 2500

33

2500 − 3000

28

3000 − 3500

30

3500 − 4000

22

4000 − 4500

16

4500 − 5000

7

Answer:

It can be observed from the given data that the maximum class frequency is 40, belonging to 1500 − 2000 intervals.

Therefore, modal class = 1500 − 2000

Lower limit (l) of modal class = 1500

Frequency (f1) of modal class = 40

Frequency (f0) of class preceding modal class = 24

Frequency (f2) of class succeeding modal class = 33

Class size (h) = 500

Therefore, modal monthly expenditure was Rs 1847.83.

To find the class mark, the following relation is used.

Class size (h) of the given data = 500

Taking 2750 as assumed mean (a), diui, and fiuiare calculated as follows.

Expenditure (in Rs)

Number of families

fi

xi

di = xi − 2750

fiui

1000 − 1500

24

1250

− 1500

− 3

− 72

1500 − 2000

40

1750

− 1000

− 2

− 80

2000 − 2500

33

2250

− 500

− 1

− 33

2500 − 3000

28

2750

0

0

0

3000 − 3500

30

3250

500

1

30

3500 − 4000

22

3750

1000

2

44

4000 − 4500

16

4250

1500

3

48

4500 − 5000

7

4750

2000

4

28

Total

200

− 35

From the table, we obtain

Therefore, mean monthly expenditure was Rs 2662.50.

Video Solution

Page No 276:

Question 4:

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher

Number of states/U.T

15 − 20

3

20 − 25

8

25 − 30

9

30 − 35

10

35 − 40

3

40 − 45

0

45 − 50

0

50 − 55

2

Answer:

It can be observed from the given data that the maximum class frequency is 10 belonging to class interval 30 − 35.

Therefore, modal class = 30 − 35

Class size (h) = 5

Lower limit (l) of modal class = 30

Frequency (f1) of modal class = 10

Frequency (f0) of class preceding modal class = 9

Frequency (f2) of class succeeding modal class = 3

It represents that most of the states/U.T have a teacher-student ratio as 30.6.

To find the class marks, the following relation is used.

Taking 32.5 as assumed mean (a), diui, and fiui are calculated as follows.

Number of students per teacher

Number of states/U.T

(fi)

xi

di = xi − 32.5

fiui

15 − 20

3

17.5

− 15

− 3

− 9

20 − 25

8

22.5

− 10

− 2

− 16

25 − 30

9

27.5

− 5

− 1

− 9

30 − 35

10

32.5

0

0

0

35 − 40

3

37.5

5

1

3

40 − 45

0

42.5

10

2

0

45 − 50

0

47.5

15

3

0

50 − 55

2

52.5

20

4

8

Total

35

− 23

Therefore, mean of the data is 29.2.

It represents that on an average, teacher−student ratio was 29.2.

Video Solution

Question 5:

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored

Number of batsmen

3000 − 4000

4

4000 − 5000

18

5000 − 6000

9

6000 − 7000

7

7000 − 8000

6

8000 − 9000

3

9000 − 10000

1

10000 − 11000

1

Find the mode of the data.

Answer:

From the given data, it can be observed that the maximum class frequency is 18, belonging to class interval 4000 − 5000.

Therefore, modal class = 4000 − 5000

Lower limit (l) of modal class = 4000

Frequency (f1) of modal class = 18

Frequency (f0) of class preceding modal class = 4

Frequency (f2) of class succeeding modal class = 9

Class size (h) = 1000

Therefore, mode of the given data is 4608.7 runs.

Video Solution

Question 6:

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

Number of cars

0 − 10

10 − 20

20 − 30

30 − 40

40 − 50

50 − 60

60 − 70

70 − 80

Frequency

7

14

13

12

20

11

15

8

Answer:

From the given data, it can be observed that the maximum class frequency is 20, belonging to 40 − 50 class intervals.

Therefore, modal class = 40 − 50

Lower limit (l) of modal class = 40

Frequency (f1) of modal class = 20

Frequency (f0) of class preceding modal class = 12

Frequency (f2) of class succeeding modal class = 11

Class size = 10

Therefore, mode of this data is 44.7 cars.


 

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