Question

select the outlier in the data set. 15 20 36 21 32 18 31 93 50 33 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 set {15, 20, 36, 21, 32, 18, 31, 93, 50, 33}, 93 is much larger than the other values.

Step2: Understand the effect on the mean

The mean of a data set is calculated as $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. When we remove an outlier that is larger than the other data - points, the sum of the remaining data - points will be smaller, and the number of data - points ($n$) 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 93. If the outlier were removed from the data set, the mean would decrease.