Question

The cumulative frequency of the class $55-58$ is how much greater than the frequency of the class $58-61$ in the following distribution?

Height (in cm)	$52-55$	$55-58$	$58-61$	$61-64$
No. of Students	$10$	$20$	$25$	$10$

(a). $2$
(b). $3$
(c). $4$
(d). $5$

Answer 1

Hint: In this problem we need to find the difference between the cumulative frequency of one class to the frequency of another class of the given distribution. For this we need to find the cumulative frequency of the class, so we will construct the cumulative frequency table. We know that the cumulative frequency of the class is the sum of frequencies of all the classes before the class. After having the cumulative frequency distribution table we can calculate the required value.

Complete step by step answer:
Given data is

Height (in cm)	$52-55$	$55-58$	$58-61$	$61-64$
No. of Students	$10$	$20$	$25$	$10$

Cumulative distribution table of the above table is given by

Height (in cm)	No. of Students (frequency)	Cumulative frequency
$52-55$	$10$	$10$
$55-58$	$20$	$10+20=30$
$58-61$	$25$	$10+20+25=55$
$61-64$	$10$	$10+20+25+10=65$

Now we have the cumulative frequency of the class $55-58$ as $30$ and the frequency of the class $58-61$ as $25$. So the required difference is given by
$30-25=5$

So, the cumulative frequency of the class $55-58$ is $5$ greater than the frequency of the class$58-61$.
So, the correct answer is “Option d”.

Note: In this problem we have asked to calculate the difference between cumulative frequency and frequency of the two different classes. In some cases we may have asked to calculate the difference between cumulative frequency and frequency of the same class. Then also we need to form the cumulative distribution table and list the required values and calculate the difference.