Calculating the new average when an item is added

It is important for students to learn how to calculate a new average when a new item is added. Remember that an average of a set of numbers is calculated by adding all the numbers and then dividing by how many numbers there are. Let us review how to calculate an average:

In four basketball matches, Khari scored 12 points, 18 points, 23 points and 7 points. Calculate the average number of points he scored in these four matches.

Working:

Total number of points scored = 12+18+23+7 = 60 points

Average number of points scored = 60 points ÷ 4 = 15 points

Therefore, after playing four matches, Khari’s average score per match is 15 points.

However, as Khari plays more games, this average is likely to change. Look at the example below:

Example 1

After playing four basketball matches, Khari’s average score is 15 points. In his fifth game, he scores 30 points. What is his average score after five games?

How do we work this out? First we must find Khari’s total score after four games. Then we add the score from the fifth game to get the total score after five games. Then we divide by 5 to find the new average. Look at the working below:

Working:

Total score after 4 games = 15 x 4 = 60 points

Total score after 5 games = 60 points + 30 points = 90 points

Average after 5 games = 90 points ÷ 5 = 18 points

Therefore Khari’s new average is 18 points.

Here are two more examples:

Example 2

Sharice earns an average of $60 each day over 5 days. On the sixth day she earns $150. What is the average amount of money she earned each day over the six days?

Working:

Total amount of money earned over 5 days = $60 x 5 = $300

Total amount of money earned in six days = $300 + $150 = $450

Average amount of money earned each day = $450 ÷ 6 = $75

Therefore the average amount of money Sharice earned each day over six days is $75.

Example 3

After three tests, Kennita’s average was 72%. She scored 96% in the fourth test. What is her new average?

Working:

Total score after 3 tests = 72 x 3 = 216

Total score after 4 tests = 216 + 96 = 312

New average after 4 tests = 312 ÷ 4 = 78

Therefore Kennita’s new average after four tests is 78%