Question

Learn with an example Select the outlier in the data set. 7 58 62 65 68 72 74 76 86 If the outlier were removed from the data set, would the mean increase or decrease?

Answer 1

An outlier is a part of the dataset that differs significantly from the rest.

Given the data:

$7,\text{ 58, 62, 65, 68, 72, 74, 76, 86}$

The outlier by observation is 7

If the outlier were removed, would the mean increase or decrease?

Mean with the outlier :

$\begin{gathered} \text{Mean = }\frac{7\text{ + 58 + 62 + 65 + 68 + 72 + 74+ 76+ 86}}{9} \\ =\frac{568}{9} \\ =\text{ 63.1} \end{gathered}$

Mean without the outlier:

$\begin{gathered} \text{Mean = }\frac{58\text{ + 62 + 65 + 68 + 72 + 74 + 76 + 86}}{8} \\ =\text{ }\frac{561}{8} \\ =\text{ 70.125} \end{gathered}$

Hence, if the outlier were removed, the mean would increase