Average sum trick

The average sum trick simply refers to the idea that if a question gives the average of a data set and the number of data points in that data set, then that also allows a student to calculate the sum of all of the data points in the set.

This is equal to: average  • # of data points

This is important to know for questions about adding or subtracting data points.

For example:

5 tests, average is 80. After the 6th test, the average is 82. What was the 6th test score?

Average Sum = 80  • 5 = 400

The new average is going to be equal to: (the old sum + the new number)/the updated # of data points

82 = 400 + 6th score6 (82•6) − 400 = 6thscore The 6th score was a 92.

This works the same for subtracting a data point. The only difference is that the denominator is reduced by 1 instead of increased by 1, and the removed test score is subtracted rather than added to the original sum.