Question

Which of the following statements is true about the median and the mean?

a. The mean is the middle number in a sorted set of observations
b. Median is a measure of the variation in a distribution
c. Extreme observations do not affect calculation of the median
d. If there is no middle number of a list of numbers, then we can say that the list does not have a median

Answer 1

The true statement is that extreme observations do not affect the calculation of the median. The median is robust to outliers as it is simply the middle value in an ordered set, or the average of the two middle values for an even number of data points.

Step-by-step explanation:

The statement that is true about the median and the mean is: Extreme observations do not affect calculation of the median. Unlike the mean, which is influenced by outliers, the median is robust against extreme values because it is the middle value in an ordered set. If a data set has an odd number of values, the median is the middle one. For even numbers of data, the median is the average of the two middle values.

Mean, on the other hand, is the sum of all observations divided by the number of observations, making it sensitive to outliers. If there is no middle number because the list of numbers is even, the median is found by taking the average of the two middle numbers after arranging the data in ascending order.