# NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4

Get the comprehensive Chapter 14 Ex 14.4 Class 10 Maths NCERT Solutions from here and score good marks in CBSE Class 10 Board Examinations.

NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 14 Statistics Class 10 NCERT Solutions Ex 14.4.

 Board CBSE Textbook NCERT Class Class 10 Subject Maths Chapter Chapter 14 Chapter Name Statistics Exercise Ex 14.4 Number of Questions Solved 3 Category NCERT Solutions

## NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4

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.

Solution:

We can find frequency distribution table of less than type as following –

 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

Now taking upper class limits of class intervals on x-axis and their respective frequencies on y-axis we can draw its ogive as following –

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.

Solution:
The given cumulative frequency distributions of less than type is –

 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

Now taking upper class limits on x-axis and their respective cumulative frequency on y-axis we may draw its ogive as following

Now mark the point A whose ordinate is 17.5 its x-coordinate is 46.5. So median of this data is 46.5.
We may observe that difference between two consecutive upper class limits is 2. Now we may obtain class marks with their respective frequencies 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

Now the cumulative frequency just greater than  is 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

So median of this data is 46.5
Hence, 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.

Solution:
We can obtain cumulative frequency distribution of more than type as following –
 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

Now taking lower class limits on x-axis and their respective cumulative frequencies on y-axis we can obtain its ogive as following.

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