Question

A bimodal data set is given as follows:

$23$	$24$	$25$	$26$	$27$	$23$	$24$
$25$	$28$	$24$	$29$	$19$	$20$	$x$

What is the possible value of $x$?

• A. $19$ or $24$
• B. $24$ or $29$
• C. $24$ or $25$
• D. $23$ or $25$

Answer 1

The correct option is D $23$ or $25$

As the given data set is bimodal, it must have two modes.

Let's arrange the data points in ascending order, except the unknown $x$.

19	20	23	23	24	24	24
25	25	26	27	28	29	$x$

As $24$ is occurring the maximum number of times, $24$ is one of the modes.

The second most occurring numbers are $23$ and $25$, which occour two times each.

$\therefore$ If one of the numbers $23$ or $25$ gets repeated exactly one more time, the data set will be bimodal data with one mode as $24$ and other mode as $23$ or $25$.

Hence, $x$ can either be $23$ or $25$.

$\bullet$ For $x=23$, the data set becomes

19	20	23	23	23	24	24
24	25	25	26	27	28	29

The above data set has two modes: $23$ and $24$.

$\bullet$ For $x=25$, the data set becomes

19	20	23	23	24	24	24
25	25	25	26	27	28	29

The above data set has two modes: $24$ and $25$.