Question

select the outlier in the data set.
23 20 27 12 11 75 15 25 19 33
24 47 26
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 {23, 20, 27, 12, 11, 75, 15, 25, 19, 33, 24, 47, 26}, most of the values are in the range of 11 - 47, and 75 is much larger than the rest. So the outlier is 75.

Step2: Analyze the effect on the mean

The mean of a data set is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The outlier 75 is larger than most of the values. When we remove it, the sum of the data values will decrease, and the number of data values ($n$) will also decrease by 1. But the proportionate decrease in the sum is larger than the decrease in $n$. So the mean will decrease.

Answer:

The outlier is 75.
Decrease