Question

The mode with outlier is , and the mode without outlier is in the data set given below.

$12,28,5,2,16,28,6,2,9,28,28$

Answer 1

In the given data set, all the data points except number $28$ lie between $0$ and $20$. So, the outlier of the given data set is $28$.

By arranging the data set with outlier in an increasing order, we get:
$2,2,5,6,8,9,12,16,28,28,28,28$

Here, $28$ is repeated four times. This is the maximum number of occurrence in the data set.

$\therefore$ The modes of the data set with outlier is $28$.

The given ordered data set without outlier:
$2,2,5,6,8,9,12,16$

Here, only number $2$ repeats twice. This is the maximum number of occurrence in the data set.

$\therefore$ The mode of the data set without outlier is $2$.