Question

select the outlier in the data set.
77 69 95 78 85 92 94 8
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 \(77,69,95,78,85,92,94,8\), the number \(8\) is much smaller than the other numbers. So the outlier is \(8\).

Step2: Analyze the effect of removing the outlier on the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Let \(S=\sum_{i=1}^{8}x_{i}=77 + 69+95+78+85+92+94+8=608\), and \(n = 8\). The original mean \(\bar{x}_{1}=\frac{608}{8}=76\).
If we remove the outlier \(8\), then \(S'=\sum_{i = 1}^{7}x_{i}=608 - 8=600\), and \(n'=7\). The new mean \(\bar{x}_{2}=\frac{600}{7}\approx85.71\)

Answer:

The outlier is \(8\) and the mean would increase.