Question

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

$10$	$9$	$5$	$2$	$6$
$4$	$3$	$7$	$5$	$5$
$6$	$7$	$1$	$7$	$0$

She mistakenly entered the number $9$. Given that the data set is trimodal data, the correct value in place of $9$ is .

Answer 1

We know that trimodal data set has three modes.

After arranging the data points in ascending order, we get

$0$	$1$	$2$	$3$	$4$
$\underset{–}{5}$	$\underset{–}{5}$	$\underset{–}{5}$	$6$	$6$
$\underset{–}{7}$	$\underset{–}{7}$	$\underset{–}{7}$	$9$	$10$

Here, the maximum number of occurrences of the numbers $5$ and $7$ is $3$.

$\therefore$ The given data set has already two modes: $5$ and $7$.

To have trimodal data, the second most occuring number $6$ must be repeated exactly one more time.

If we replace the number $9$ with $6$, the occurrences of $6$ will be thrice as shown below.

$0$	$1$	$2$	$3$	$4$
$\underset{–}{5}$	$\underset{–}{5}$	$\underset{–}{5}$	$\underset{–}{6}$	$\underset{–}{6}$
$\underset{–}{6}$	$\underset{–}{7}$	$\underset{–}{7}$	$\underset{–}{7}$	$10$

And, the above data set has three modes: $5$, $6$ and $7$.

$\therefore$ Amelia had mistakenly entered $6$ as $9$.