Question

The total marks in the fourth class interval is ………………

Class interval	$30 - 40$	$40 - 50$	$40 - 50$	$60 - 70$	$70 - 80$	$70 - 80$
Marks	$1$	$2$	$4$	$5$	$6$	$7$

$A)2$
$B)4$
$C)12$
$D)16$

Answer 1

First we define the cumulative frequency then we just use that concept, we follow that step. Finally we get the fourth class interval of the total mark.

Complete step-by-step solution:
It is given the data for class intervals and marks.
Here we have to find out the total marks in the class fourth that is we need to find the cumulative frequency
Let us first define the cumulative frequency.
The cumulative frequency analysis of the frequency of occurrence value of a phenomenon less than a reference value.
The cumulative frequency is also called the frequency of the non- exceedance.
Cumulative frequency can be also defined as the sum of all the previous frequencies up to the current value.
So we are draw cumulative frequency table as below:

Class Interval	Marks (frequency)	Cumulative Frequency
$30 - 40$	$1$	$1$
$40 - 50$	$2$	$1 + 2 = 3$
$50 - 60$	$4$	$3 + 4 = 7$
$60 - 70$	$5$	$7 + 5 = 12$

Here $1$ is the first frequency for the interval $30 - 40$, the cumulative frequency for the first group would be same which is $1.$
So for the second group the next class interval, $40 - 50$ here is the frequency is $2$ now the value of the above two frequencies is to be added like $1 + 2 = 3$, Hence we get $3$ which is the cumulative frequency for the second group.
Further we just followed the same patterns and just added the previous value for the group.
Finally we achieved the cumulative frequency for the last group is $12$.
So this is how cumulative frequency is determined.
Hence the fourth class interval is $12.$

Therefore the correct option is $(C)$ that is $12.$

Note: Cumulative frequency helps to determine the number of operations lying above specific observation. Commutative property is an important tool in the statistics to tabular data in an organized manner.
Whenever you wish to find out the popularity of a certain type of data, or the likelihood that a given event will fall within certain frequency distribution, a cumulative frequency table can be most useful.
Say it for example, the Census department has collected data and wants to find out all the residents in the city aged below $45$. In this given case, a cumulative frequency table will be helpful.