# Statistics

## NCERT Exercise 14.4

Question 1. The following distribution gives the daily income of 50 workers of a factory.

 Daily income (in Rs) Number of workers 100-120 120-140 140-160 160-180 180-200 12 14 8 6 10

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

Solution:

Daily incomeCumulative frequency
Less than 12012
Less than 14026
Less than 16034
Less than 18040
Less than 20050 Question 2. During the medical checkup of 35 students of a class, their weights were recorded as follows:

Weight (in kg)Number of students
Less than 380
Less than 403
Less than 425
Less than 449
Less than 4614
Less than 4828
Less than 5032
Less than 5235

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.

Solution: Weight (in kg)FrequencyCumulative Frequency
36-3800
38-4033
40-4225
42-4449
44-46514
46-481428
48-50432
50-52335

Since N = 35 and n/2 = 17.5 hence median class = Less than 46-48

Here; l = 46, cf = 14, f = 14 and h = 2

Median can be calculated as follows:

text(Median)=l+(n/2-cf)/(f)xxh

=46+(17.5-14)/(14)xx2

=46+1/2=46.5

This value of median verifies the median shown in ogive.

Question 3. The following table gives production yield per hectare of wheat of 100 farms of a village.

 Production yield (in kg) Number of farms 50-55 55-60 60-65 65-70 70-75 75-80 2 8 12 24 38 16

Change this distribution to a more than type distribution, and draw its ogive.

Solution:

Production yieldCumulative frequency
More than 50100
More than 5598
More than 6090
More than 6578
More than 7054
More than 7516 