How Changing a Value Affects the Mean and Median

In this lesson we are given a data set. We find it’s mean and median. Then one of its data is changed. We then find the changed mean and changed median after one of the data has been changed.

Find new mean and new median of the data set if a data is changed.

12, 15, 18, 13, 6, 14; 13 is changed to 5

Solution

Step 1:

Mean = $\frac{(12 + 15 + 18 + 13 + 6 + 14)}{6}$ = 13; Median = 13.5

Step 2:

With data change

New Mean = $\frac{(12 + 15 + 18 + 5 + 6 + 14)}{6}$ = 11.67; New Median = 13

Find new mean and new median of the data set if a data is changed.

18, 15, 11, 3, 8, 4, 13, 12, 3; 15 is changed to 18

Solution

Step 1:

Mean = $\frac{(18 + 15 + 11 + 3 + 8 + 4 + 13 + 12 +3)}{9}$ = 9.67; Median = 11

Step 2:

With data change

New Mean = $\frac{(18 + 18 + 11 + 3 + 8 + 4 + 13 + 12 +3)}{9}$ = 10 ; New Median = 11