Class 10 Mathematics

Statistics

Exercise 14.4(NCERT)

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

Daily income (in Rs)100-120120-140140-160160-180180-200
Number of workers12148610

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
statistics exercise 4 question 1 ogive

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:

statistics exercise 4 question 2 ogive
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.

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

Production yield (in kg)50-5555-6060-6565-7070-7575-80
Number of farms2812243816

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
statistics exercise 4 question 3 ogive
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Introduction

Exercise 1

Exercise 2

Exercise 3