Question

select the outlier in the data set.
6 53 55 60 63 67 68 69 70 71
73 75 77 78 79 81 82 88 92 98
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 this data set, 6 is much smaller than the other values.

Step2: Analyze the effect on the mean

The mean is calculated as $\frac{\text{sum of all data points}}{\text{number of data points}}$. The outlier 6 is a very small value. When it is removed, the sum of the data points will increase (since we are removing a small value) and the number of data points will decrease by 1. But the increase in the sum (by removing a small number) has a more significant impact. Let's assume the sum of all data points is $S$ and the number of data points is $n$. The original mean is $\overline{x}_1=\frac{S}{n}$. After removing 6, the new sum is $S - 6$ and the new number of data points is $n-1$. The new mean is $\overline{x}_2=\frac{S - 6}{n - 1}$.

We can also think of it in a simple way: since 6 is below the general range of the other data points, removing it will make the average of the remaining data points larger.

Answer:

increase