Chapter 10.2, Problem 16HP

To determine

To check: If the statement that of mean, median and mode, the mean will always be most affected by the outliers is true or not and to give a counterexample if statement is false.

Answer to Problem 16HP

The given statement is false.

Explanation of Solution

Given information: Statement is regarding central tendencies and outliers.

The mean is usually most affected by the outliers, but not always. For e.g., consider the data set $\{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,17,18,200,200\}$ }. Here $200$ is an outlier that is repeated two times.

Mean of this data set $=29.35$

Mean of data set without outliers $=10.39$

Mode of this data set $=200$

Mode of data set without outliers $=17$

Thus, the mode is most affected in this case by the outliers.

Thus, the given statement is false.