Question

The difference between the median of the numbers $7,5,4,8,9,25$ with and without outlier is .

Answer 1

Observe the given data, the outlier of this data is $25$ as it is very different from the rest of the values of the data set.

Arrange the given data in ascending order.


Here, the number of values is even, therefore median is calculated by taking the mean of these two middle numbers, i.e., $7$ and $8$.

$\begin{array}{cc}\text{Median}& =\text{Mean of two middle numbers}\\ & =\frac{7+8}{2}\\ & =\frac{15}{2}\\ & =7.5\end{array}$

Thus, the median with outlier is $7.5$.

Now, observe the given data without outlier.


Since, the middle number is $7$, therefore the median of this data is $7$.

Hence, the median without outlier is $7$.

Thus, the difference between the median with and without outlier is calculated as,

$\begin{array}{cc}\text{Required difference}& =\text{Median with outlier}-\text{Median without outlier}\\ & =7.5-7\\ & =0.5\end{array}$

Hence, the difference between the median with and without outlier for the given data set is $0.5$.