Question

The demand for different shirt sizes is given in the table.

Size	$38$	$39$	$40$	$41$	$42$	$43$	$44$
No. of persons	$26$	$36$	$20$	$15$	$13$	$7$	$5$

Find the modal shirt size.
${\text{(A)}}$ $39$
$\left( {\text{B}} \right)$ $40$
$\left( {\text{C}} \right)$ $44$
$\left( {\text{D}} \right)$ $42$

Answer 1

Here, we have to find mode we should look through the observation which occurs the most. In all problems with ungrouped data (i.e.) observations which have no class limits, the mode of the problem should be found in the following method. Just look through the question once or twice, the answer is very simple.

Complete step-by-step solution:
From the above table, the size of different shirts and the respective number of persons purchased the shirts are also given.

Size	No. of persons
$38$	$26$
$39$	$36$
$40$	$20$
$41$	$15$
$42$	$13$
$43$	$7$
$44$	$5$

So, it is clear that the highest number of people has occurred in the shirt size $39$ compared with other shirt sizes.
(i. e) $36$ persons demanded the shirt size of $39$
Other shirt sizes such as $38$,$40$,$41$,$42$,$43$ & $44$ have lower frequencies than the shirt size of $39$.
We have the formula for mode as mentioned below,
Mode = highest occurring observation.
$\therefore$ Mode = $39$
So, the modal shirt size is $39$

Hence, the correct answer is (A).

Note: Here, the modal shirt size has been found by the No. of persons demanding the shirts. Similar methods can be applied to find the mode value of other problems.
Mode is an important tool in statistics which is used to interpret data in a relevant manner.
Although it is an essential thing in statistics, mode can be found by simple strategies.
There may be a multimodal data in which there will be more than one mode in a group of observations. So, their answer will be one or more values.