Question

Select the outlier in the data set.22324041576268752If the outlier were removed from the data set, would the mean increase or decrease?increasedecrease

Answer 1

An outlier is a value that is much larger or smaller in a set of data.

In this case, you can see that the value that is much larger than the other data is 752.

Therefore, the outlier in the data set is 752.

On the other hand, let us find the mean of the data set with and without the outlier to see if it increases or decreases.

The formula to find the mean of a data set is:

`\text{Mean }=\frac{\text{ Sum of data points}}{\text{Number of data points}}`

Then, we have:

• Data set with the outlier

`\begin{gathered} \text{Mean }=(22+32+40+41+57+62+68+752)/(8) \\ \text{Mean }=(1074)/(8) \\ \boldsymbol{Mean=134.25} \end{gathered}`

• Data set without the outlier

`\begin{gathered} \text{Mean }=(22+32+40+41+57+62+68)/(8) \\ \text{Mean }=(322)/(7) \\ \boldsymbol{Mean=46} \end{gathered}`

As you can see, if the outlier was removed from the data set, the mean goes from 134.25 to 46. Therefore, the mean decreases.