Question

What will happen to the measures of central tendency if the outlier is removed?4, 5, 5, 6, 7, 8, 17They will not change.The mean will increase.The mean will decrease.The mode will change.

Answer 1

The mean will decrease

Explanation

An outlier is an observation that lies an abnormal distance from other values in a dataset. In the case of the dataset:

4, 5, 5, 6, 7, 8, 17

the outlier is 17

The mean is calculated as follows:

`mean=\frac{sum\text{ of terms}}{number\text{ of terms}}`

Then, the mean of the original dataset is:

`\begin{gathered} mean=(4+5+5+6+7+8+17)/(7) \\ mean=(52)/(7) \\ mean\approx7.4 \end{gathered}`

After 17 is removed from the set, the mean is:

`\begin{gathered} mean=(4+5+5+6+7+8)/(6) \\ mean=(35)/(6) \\ mean\approx5.8 \end{gathered}`

The mean will decrease if the outlier is removed