Question

The shirt sizes worn by a group of $200$ persons, who bought the shirt from a store, are as follows:

Shirt size	$37$	$38$	$39$	$40$	$41$	$42$	$43$	$44$
Number of persons	$15$	$25$	$39$	$41$	$26$	$17$	$15$	$12$

Find the modal shirt size worn by the group.

Answer 1

Hint: In this question, we are given a table which has shirt sizes and the number of persons who wear that size. We have been asked to find the modal size of the group. We know that mode is the most frequently occurring value. So, observe that size which is worn by most of the people and that size will be our mode.

Complete step-by-step solution:
We are given a table with shirt sizes and the number of persons who wear that size. Before finding mode, let us understand in brief what mode is.
Mode is one of the measures of central tendency and is probably the easiest to find out of all. It is that value of the data which occurs the most. Basically, it is the most frequently occurring value. Though it is easy to understand and calculate, it has a lot of disadvantages as it does not represent the entire data. It does not take into account all the values and is useful particularly for qualitative data. Other measures of central tendency are mean and median.
Now, moving towards our question. Let’s draw the table once.

Shirt size	$37$	$38$	$39$	$40$	$41$	$42$	$43$	$44$
Number of persons	$15$	$25$	$39$	$41$	$26$	$17$	$15$	$12$

If we observe carefully, we will be able to see that the shirt size - $40$ has the highest frequency. It is the most occurring size out of all the sizes.

$\therefore $ The modal shirt size of the data is $40$.

Note: If in a question, there are two observations with the highest frequency, then both the observations will be considered as the mode. In this case, the set is called bimodal. Hence, it is not necessary that the set has only one mode.