Question

Consider the data set: $16,14,15,19,14,18,12,14$

If 1 is included in the data set, what would be the effect on the median of the dataset?

• A. Median will increase.
• B. Median will decrease.
• C. Median will be the same.

Answer 1

The correct option is B Median will decrease.

Data set in increasing order without including $20$ : $12,14,14,14,15,16,18,19$

The median of data set $=$ mean of $4^{th}\&5^{th}$ position

$=\frac{14+15}{2}=14.5$

Data set in increasing order including $1$ : $1,12,14,14,14,15,16,18,19$

The median of data set $=14$

We can see on including $1,$ the median of the dataset decreased.

In the data set : $1,16,14,15,19,14,18,12,14$

$\Rightarrow 1$ is the outlier.