Question

select the outlier in the data set. 8 52 56 60 63 64 65 67 77 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 {8, 52, 56, 60, 63, 64, 65, 67, 77}, 8 is much smaller than the other values. So the outlier is 8.

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 8 is a very small value. When it is removed, the sum of the remaining data - points will be larger relative to the number of data - points (since $n$ decreases by 1 but the sum decreases by a small amount compared to the total sum without 8). So the mean will increase.

Answer:

The outlier is 8.
The mean will increase.