Question

Find out the modal class for the following table:

X	1-3	3-5	5-7	7-9	9-11
frequency	2	6	4	3	5

A) 1−3
B) 3−5
C) 5−7
D) 7−9

Answer 1

We will start solving the problem by checking whether the given data in the frequency table is continuous or not. If the data is continuous, we will proceed further to find the modal class, otherwise we add the correction factor to lower and upper boundaries of the class intervals to make it continuous. For the modal class, we will find the class corresponding to the highest frequency in the frequency distribution table.

Complete step by step solution:
Here we need to find the modal class of the given data.

X	1-3	3-5	5-7	7-9	9-11
frequency	2	6	4	3	5

From the frequency table, we can see that the upper limit of the previous class interval is equal to the lower limit of the next class interval. This makes the given data in the frequency table continuous.
First, we will find the highest frequency in the frequency distribution table.
Here 6 is the highest frequency in the frequency distribution table and we know that the modal class is the class which is corresponding to the highest frequency in the frequency distribution table.
The class which is corresponding to the highest frequency 6 in the table is $3 - 5$.

Thus, the correct option is option B.

Note:
Here we have obtained the modal class for the given frequency distribution table. We need to keep in mind that to determine the modal class, we will first determine the highest frequency in the frequency table. Then we will find the class associated with the highest frequency. Modal class is used in determining the mode for the frequency distribution table.