Total-Average-Number

1) Never Average Averages

You cannot find the average of multiple averages by combining the averages.
In order to avoid this trap, combine the sums of sets and calculate the overall average by dividing the combined sum by the combined number.

For example:

If Tommy averaged 20 points for 3 basketball games and averaged 30 in the next 2, what was his average for all five games?

1. First, calculate the total points scored:
   1. 20 * 3 = 60
   2. 30 * 2 = 60
   3. 60 + 60 = 120
2. Second, calculate the total number of games played:
   • 2 + 3 = 5
3. Last, divide the total points scored by the total number of games:
   • ¹²⁰ ⁄ ₅ = 24

2) Practice:

If Alice averages 25 points in her first 4 basketball games, what must she average in the next 2 games to raise her overall average to 30 points per game?

1. 27.5
2. 30
3. 32.5
4. 37.5
5. 40