Question

select the outlier in the data set.
38 30 39 14 17 29 22 20 99 32
if the outlier were removed from the data set, would the mean increase or decrease?
increase decrease

Explanation:

Step1: Identify the outlier

An outlier is a data - point that is significantly different from other data - points. In the data set {38, 30, 39, 14, 17, 29, 22, 20, 99, 32, 26}, 99 is much larger than the other values.

Step2: Analyze the effect on the mean

The mean of a data set is the sum of all data points divided by the number of data points. The outlier 99 is a large value. When we calculate the mean with 99 included, it pulls the mean up. If we remove 99, the sum of the remaining data points will be smaller, and since the number of data points also decreases by 1, but the reduction in the sum is relatively large compared to the reduction in the number of data points. So the mean will decrease.

Answer:

Outlier: 99
Effect on mean: decrease