Average Goals Challenge: Math in Sports

A team scores 3, then 1, then 4, then 2, then 5. Are they any good? Five separate numbers are hard to hold in your head, and harder still to compare with another team's five. An average squashes them into one number you can actually use.

Working One Out

An average is the total shared out evenly, as if every game had gone the same way.

A basketball player scores 10, then 12, then 8.

• Add them: 10 + 12 + 8 = 30
• Count the games: 3
• Divide: 30 ÷ 3 = 10

Their average is 10 points a game — even though they never actually scored exactly 10 in any of them. That is worth noticing. An average does not have to be a score anyone really got.

A Whole Season

Team Awesome's last five games: 3 goals, 1 goal, 4 goals, 2 goals, 5 goals.

• Add them: 3 + 1 + 4 + 2 + 5 = 15
• Count the games: 5
• Divide: 15 ÷ 5 = 3

Three goals a game. Now you have one number you can compare with any other team, however many games they have played.

Your Turn

Team Rocket's last four games: 2 goals, 0 goals, 3 goals, 1 goal.

Work out their average before you look. Add the four numbers, then divide by four. Watch out for that 0 — it is a real game and it still counts, so the number you divide by is 4, not 3.

The total is 6 and there were 4 games, so 6 ÷ 4 = 1.5. Half a goal is impossible in a real match, and the average is still 1.5 — another sign that an average describes the set of games rather than any one of them.

Team Awesome average 3 and Team Rocket average 1.5, so Team Awesome score twice as often. That comparison is the entire point of doing this.

Go and Try It On Something Real

Averages work on anything you can count more than once. How many minutes you read each night this week. Goals your own team scored. Cups of water you drink in a day.

Count for a week, add, divide by 7. The answer will probably surprise you, because most people are bad at guessing their own averages.