Question

select the outlier in the data set. 81 83 54 77 259 72 75 64 87 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 {81, 83, 54, 77, 259, 72, 75, 64, 87}, 259 is much larger than the other values.

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 259 is a large value. When it is removed, the sum of the data values $\sum_{i = 1}^{n}x_{i}$ will decrease by a 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:

259
decrease