Question

1. what effect will the outlier have on the mean of the data if the outlier is excluded? 5, 8, 9, 7, 10, 6, 25

Explanation:

Step1: Identify the outlier

The outlier is 25 as it is far from other values.

Step2: Calculate the mean with all data

The sum of all data $5 + 8+9 + 7+10+6 + 25=70$. There are 7 data - points. The mean $\bar{x}_1=\frac{70}{7}=10$.

Step3: Calculate the mean without the outlier

The sum of data without 25 is $5 + 8+9 + 7+10+6=45$. There are 6 data - points. The mean $\bar{x}_2=\frac{45}{6}=7.5$.

Step4: Analyze the effect

The difference in means is $10 - 7.5 = 2.5$. The mean decreases by 2.5 when the outlier is excluded.

Answer:

The mean decreases by 2.5.