Question

Under which circumstances below is the median likely to be a better measure of central tendency than the mean?

a) When the distribution is symmetric
b) When the distribution is positively skewed
c) When there are extreme outliers
d) When the data is normally distributed

Answer 1

The median is a better measure of central tendency than the mean in distributions that are positively skewed or contain extreme outliers, as the mean is influenced by these factors while the median is not.

Step-by-step explanation:

The circumstances under which the median is likely to be a better measure of central tendency than the mean is when a distribution is positively skewed or there are extreme outliers within the data set. This is because the mean is affected by every single value in the data set, which includes the outliers and skewed data, so it tends to be pulled toward the tail. Therefore, in a positively skewed distribution, the mean will be greater than the median. Conversely, when the data is symmetric or normally distributed, the mean and median are close to each other and can both be good measures of central tendency.

In summary, the median is particularly useful when dealing with skewed distributions or outliers, as it represents the middle point of the data without being influenced by extreme values, unlike the mean.