Question

What type of cumulative frequency table is given?

Marks	Number of students	Cumulative frequency (cf)
$0-10$	$4$	$4$
$10-20$	$6$	$4+6=10$
$20-30$	$12$	$10+12=22$
$30-40$	$8$	$22+8=30$

A. less than
B. more than
C. equal to
D. greater than

Answer 1

Hint: Here we have been given a cumulative frequency table and we have to find which type of cumulative frequency it is. Firstly we will see the cumulative frequency column and find how the values of that column are calculated. Then according to the definition of two types of cumulative frequency we will conclude our answer.

Complete answer: The cumulative frequency table is given as follows:

Marks	Number of students	Cumulative frequency (cf)
$0-10$	$4$	$4$
$10-20$	$6$	$4+6=10$
$20-30$	$12$	$10+12=22$
$30-40$	$8$	$22+8=30$

Now as we can see that in the cumulative frequency column the frequency is added from the lowest class to the highest class that is from the top to the bottom.
As we know, a less than cumulative frequency distribution is obtained by adding successively the frequencies of all the previous classes including the class against which it is written.
So it is a less than cumulative frequency distribution.
Hence the correct option is (A).

Note:
Cumulative frequency is the sum of all the frequencies of a given table, that is the frequency of the first class is added to the second class and it is written in front of the second class similarly frequency of the sum of first three class frequencies is written in front of third class and so on. There are two types of cumulative frequencies: first is the less than cumulative frequency which is already defined above and second is the more than cumulative frequency where the sum of the frequencies is started from the highest interval to the lowest that is from the bottom to the top.