Chapter 13.1, Problem 16HP

To determine

To construct: a data set with a mean of 4 and a median that is not 4.

Explanation of Solution

Let’s consider the series, with both mean and median value as 4.

1, 2, 3, 4, 5, 6, 7

In case of odd number of observation, middle value of the data is median.

  $\text{Mean=Sum}\text{of}\text{data}\text{values/Number}\text{of}\text{observation}$

Therefore both mean and median of this data is 4.

Now from the series, if we subtract 1 from the middle value, and add 1 to the last value.

1, 2, 3, 3, 5, 6, 8

Sum of data value and number of observation remain unchanged, and there would be no change in the mean value.

However middle value will change from 4 to 3.

Hence for series 1, 2, 3, 4, 5, 6, 7

Mean is 4 but median is not 4.