Question

Amelia was feeding the data points of a data set as follows:

$46$	$25$	$23$	$24$	$6$
$4$	$3$	$21$	$25$	$42$
$25$	$12$	$24$	$23$	$23$

She mistakenly entered the number $42$. Given that the data set is trimodal data, the correct value in place of $42$ is .

Answer 1

We know that trimodal data set has three modes.

After arranging the data points in ascending order, we get

$3$	$4$	$6$	$12$	$21$
$\underset{–}{23}$	$\underset{–}{23}$	$\underset{–}{23}$	$24$	$24$
$\underset{–}{25}$	$\underset{–}{25}$	$\underset{–}{25}$	$42$	$46$

Here, the maximum number of occurrences of the numbers $23$ and $25$ is $3$.

$\therefore$ The given data set has already two modes: $23$ and $25$.

To have trimodal data, the second most occuring number $24$ must be repeated exactly one more time.

If we replace the number $42$ with $24$, the occurrences of $24$ will be thrice as shown below.

$3$	$4$	$6$	$12$	$21$
$\underset{–}{23}$	$\underset{–}{23}$	$\underset{–}{23}$	$\underset{–}{24}$	$\underset{–}{24}$
$\underset{–}{24}$	$\underset{–}{25}$	$\underset{–}{25}$	$\underset{–}{25}$	$46$

And, the above data set has three modes: $23$, $24$ and $25$.

$\therefore$ Amelia had mistakenly entered $24$ as $42$.