Question

What effect will the presence of the outlier in the data set below have on the mean of the data set?

{78, 99, 85, 92, 97, 90, 89, 27, 97, 72, 75, 83, 91, 96}

A.The outlier will make the mean significantly greater than it would have been without the outlier.
B.The outlier will make the mean significantly less than it would have been without the outlier.
C.The outlier will have no significant effect on the mean of the data set.
D.No outlier exists in this data set.

Answer 1

The outlier clearly is the 27.
With it, the mean is 83,6; without it, it is greater: 88.

Is that a significant difference? I would say not, because there are values in the data set well below and above both averages.

Hence my answer would be C. If you think the difference is significant, the answer would obviously be A.

Answer 2

B.The outlier will make the mean significantly less than it would have been without the outlier.

Explanation:

An outlier is an abnormal value or observation that is distant from other values in a random sample or data.

From the given data, the outlier clearly is the 27.

Calculating the mean of the data with the outlier;

=
`(78 + 99 + 85 + 92 + 97 + 90 + 89 + 27 + 97 + 72 + 75 + 83 + 91 + 96)/(14)`

=
`(1171)/(14)`

= 83.64

The mean of the data with the outlier is 83.64.

Calculating the mean of the data without the outlier;

=
`(78 + 99 + 85 + 92 + 97 + 90 +89 +97 +72 +75 +83 + 91 +96)/(13)`

=
`(1144)/(13)`

= 88

The mean of the data without the outlier is 88.

There is a significant difference comparing the two values of the mean of the given data with or without the outlier. Thus, the mean is affected by the outlier.