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NCERT solution class 10 chapter 15 Statistics exercise 15.4 mathematics

EXERCISE 15.4


Page No 293:

Question 1:

The following distribution gives the daily income of 50 workers of a factory.

Daily income (in Rs)

100 − 120

120 − 140

140 − 160

160 − 180

180 − 200

Number of workers

12

14

8

6

10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Answer:

The frequency distribution table of less than type is as follows.

Daily income (in Rs)

(upper class limits)

Cumulative frequency

Less than 120

12

Less than 140

12 + 14 = 26

Less than 160

26 + 8 = 34

Less than 180

34 + 6 = 40

Less than 200

40 + 10 = 50

Taking upper class limits of class intervals on x-axis and their respective frequencies on y-axis, its ogive can be drawn as follows.


Question 2:

During the medical check-up of 35 students of a class, their weights were recorded as follows:

Weight (in kg)

Number of students

Less than 38

0

Less than 40

3

Less than 42

5

Less than 44

9

Less than 46

14

Less than 48

28

Less than 50

32

Less than 52

35

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.

Answer:

The given cumulative frequency distributions of less than type are

Weight (in kg)

upper class limits

Number of students

(cumulative frequency)

Less than 38

0

Less than 40

3

Less than 42

5

Less than 44

9

Less than 46

14

Less than 48

28

Less than 50

32

Less than 52

35

Taking upper class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows.

Here, n = 35

So,  = 17.5

Mark the point A whose ordinate is 17.5 and its x-coordinate is 46.5. Therefore, median of this data is 46.5.

It can be observed that the difference between two consecutive upper class limits is 2. The class marks with their respective frequencies are obtained as below.

Weight (in kg)

Frequency (f)

Cumulative frequency

Less than 38

0

0

38 − 40

3 − 0 = 3

3

40 − 42

5 − 3 = 2

5

42 − 44

9 − 5 = 4

9

44 − 46

14 − 9 = 5

14

46 − 48

28 − 14 = 14

28

48 − 50

32 − 28 = 4

32

50 − 52

35 − 32 = 3

35

Total (n)

35

The cumulative frequency just greater thanis 28, belonging to class interval 46 − 48.

Median class = 46 − 48

Lower class limit (l) of median class = 46

Frequency (f) of median class = 14

Cumulative frequency (cf) of class preceding median class = 14

Class size (h) = 2

Therefore, median of this data is 46.5.

Hence, the value of median is verified.

Question 3:

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

Production yield (in 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 ogive.

Answer:

The cumulative frequency distribution of more than type can be obtained as follows.

Production yield

(lower class limits)

Cumulative frequency

more than or equal to 50

100

more than or equal to 55

100 − 2 = 98

more than or equal to 60

98 − 8 = 90

more than or equal to 65

90 − 12 = 78

more than or equal to 70

78 − 24 = 54

more than or equal to 75

54 − 38 = 16

Taking the lower class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be obtained as follows.


 

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