Question

If $20$ is included in the data set $\{50,56,56,58,62\}$,
the mean of the dataset .

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

Answer 1

The correct option is B will decrease

The mean of the data set without including $20$ is
$\frac{50+56+56+58+62}{5}$
$=\frac{282}{5}$
$=56.4$
The mean of the data set after including $20$ is
$\frac{50+56+56+58+62+20}{6}$
$=\frac{302}{6}$
$=50.33$

So, we get the mean of the data set
$\bullet$ without including $20$= $56.4$
$\bullet$ after including $20$= $50.33$

$\therefore$ On including $20$, the mean of the dataset is decreased.

$\underset{–}{\text{Note:}}$ In the below given data set, all the numbers except $20$ lie in between $50$ and $65$. So, the outlier of the given data set is $20$.

$\underset{–}{20}$

$50$

$56$

$56$

$58$

$62$

$\therefore$ For the given data set, the mean with outlier (having a minimum value in the dataset) is less than the mean without an outlier.