Question

select the outlier in the data set. 34 27 23 82 44 19 35 15 10 16 26 33 46 25 30 29 21 18 14 if the outlier were removed from the data set, would the mean increase or decrease? increase decrease

Explanation:

Step1: Identify the outlier

The outlier is a value that is much larger or smaller than the other values in the data - set. In the set {34, 27, 23, 82, 44, 19, 35, 15, 10, 16, 26, 33, 46, 25, 30, 29, 21, 18, 14}, the value 82 is much larger than the rest of the values. So the outlier is 82.

Step2: Analyze the effect on the mean

The mean of a data - set is calculated as $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The outlier 82 is a large value. When we remove it from the data - set, the sum of the remaining values will be smaller than the sum of all the original values, and the number of data points $n$ will also decrease by 1. But since 82 is a large value, the sum will decrease more proportionally than the decrease in $n$. So the mean will decrease.

Answer:

The outlier is 82.
If the outlier were removed from the data set, the mean would decrease.