Question

The mode(s) of the following data set is(are) .

$11$	$19$	$20$	$11$	$12$
$16$	$15$	$19$	$18$	$13$

• A. $11$ and $19$
• B. Only $11$
• C. Only $19$

Answer 1

The correct option is A $11$ and $19$

Step 1:

Let's arrange the given data set in ascending order.

11	11	12	13	15
16	18	19	19	20

Step 2:

The frequency table of the above data set is as follows.
Frequency Table

Number	Frequency	Number	Frequency
$\underset{–}{11}$	$\underset{–}{2}$	$16$	$1$
$12$	$1$	$18$	$1$
$13$	$1$	$\underset{–}{19}$	$\underset{–}{2}$
$15$	$1$	$20$	$1$

From the above frequency table, it is very clear that the numbers $11$ and $19$ appear the most number of times in the given data set.

Hence, the modes of the given data set are $11$ and $19$.

$\underset{–}{\text{Note:}}$ Any data set with two modes is called $\text{bimodal data}$. As the given data set has two modes, $11$ and $19$, it is bimodal data set.