Question

select the outlier in the data set. 40 36 94 38 42 41 20 68 46 30 22 67 13 34 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 given data set {40, 36, 94, 38, 42, 41, 20, 68, 46, 30, 22, 67, 13, 34}, most of the values are in the range of 13 - 68, but 94 is much larger than the rest. So the outlier is 94.

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. Let the sum of all data points be \(S\) and the number of data points be \(n\). The mean \(\bar{x}=\frac{S}{n}\). When the outlier (a large value) is removed, the sum \(S\) will decrease by a relatively large amount, and the number of data points \(n\) will decrease by 1. Since the outlier is a large value, removing it will decrease the sum more proportionally than the decrease in the number of data - points. So the mean will decrease.

Answer:

The outlier is 94.
The mean will decrease.