Question

7 which measure of central tendency is most affected by outliers? i.e. it should not be used when the data is skewed. a mean b median c mode

Explanation:

• The mean is calculated as the sum of all values divided by the number of values. Outliers (extremely large or small values) can significantly pull the mean up or down. For example, in a data set like {1, 2, 3, 4, 100}, the mean is $\frac{1 + 2 + 3 + 4 + 100}{5}=\frac{110}{5} = 22$, which is heavily influenced by the outlier 100.
• The median is the middle value when data is ordered, so it is resistant to outliers. In the same data set, the ordered set is {1, 2, 3, 4, 100}, and the median is 3, unaffected by 100.
• The mode is the most frequent value, and outliers do not impact it as they are usually unique or not the most frequent.

Answer:

A. Mean