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NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10

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NCERT TEXTBOOK QUESTIONS SOLVED
Page No. 293
EXERCISE 14.4
Q 1. The following distribution gives the daily income of 50 workers of a factory 

NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Sol. We have the cumulative frequency distribution as:

Daily income (in Rs )

Cumulative frequencies

Less than 120

12 + 0 = 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

Now, we plot the points corresponding to the ordered pairs (120, 12), (140, 26), (160, 34), (180, 40) and (200, 50) on a graph paper and join them by a free hand smooth curve as shown below:
NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10
The curve so obtained is called the less than o give.

Q 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 and verify the result by using the formula
Sol. Here, the values 38, 40, 42, 44, 46, 48, 50 and 52 are the upper limits of the respective class intervals.
We plot the points (ordered pairs) (38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32) and (52, 35) on a graph paper and join them by a free hand smooth curve.
The curve so obtained is the less than type ogive.
∵ n = 35
NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10
The point 17.5 is on y-axis.
NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10
From this point (i.e., from 17.5) we draw a line parallel to the x-axis which cuts the curve at P. From this point (i.e., from P), draw a perpendicular to the x-axis, meeting the x-axis at Q. The point Q represents the median of the data which is 47.5.
Verification
To verify the result using the formula, let us make the following table in order to find median using the formula:

Weight (in kg)

Number of students [Cumulative frequency]

0-38

0

38-40

3

40-42

5

42-44

9

44-46

14

46-48

28

48-50

32

50-52

35

Here,
NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10
Since, this observation lies in the class 46 − 48.
∴ The median class is 46 − 48 such that l = 46, h = 2, f = 14, cf = 14
NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, the median = 46.5 kg is approximately verified.

Q 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 its ogive.
Sol. For ‘more than type’ distribution, we have:

Production yield (in kg/ha)

Number of farms (Cumulative frequencies)

More than 50

100

More than 55

98

More than 60

90

More than 65

78

More than 70

54

More than 75

16

Now, we plot the points (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16) and join the points with a free hand curve.
NCERT Solutions: Statistics (Exercise 14.4) Notes | Study Mathematics (Maths) Class 10 - Class 10
The curve so obtained is the ‘more than type ogive’.

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