Question

select the outlier in the data set.
9 69 81 84 85 86 90 98 99
if the outlier were removed from the data set, would the mean increase or decrease?
increase decrease

Explanation:

Step1: Calculate the original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 9$, and $\sum_{i=1}^{9}x_{i}=9 + 69+81+84+85+86+90+98+99=601$. So the original mean $\bar{x}_{1}=\frac{601}{9}\approx66.78$.

Step2: Remove the outlier and calculate the new mean

The outlier is $9$. After removing it, $n = 8$, and $\sum_{i = 1}^{8}x_{i}=601 - 9=592$. The new mean $\bar{x}_{2}=\frac{592}{8}=74$.

Answer:

increase