Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
Three friends have marbles: 5, 7 and 6, and the fourth has 2. Question: if they pooled all their marbles and shared them fairly, how many would each one get? That is exactly the idea of the mean: fair sharing.
To work out a mean, just two steps. First, add up all the values: that is the total. Then, divide this total by the number of values. Here: 5 + 7 + 6 + 2 = 20, then 20 divided by 4 equals 5. On average, each friend has 5 marbles.
The mean is a value that sums up the series: it is not necessarily equal to one of the original values, and it can even be a decimal number. The mean of 5 and 8 is 6.5, and that is perfectly normal: nobody has 6.5 marbles, but this number describes the general level well.
Watch out for the most common trap: you always divide by the number of values, even when some values repeat. For the series 5, 5, 5, 9, there are 4 values, so you divide by 4, not by 2.
The mean is useful everywhere: grades, temperatures, race times, video game scores. Learn to compute it quickly and correctly, and you will be able to sum up any series of numbers with a single value.
Your last three game scores are 12, 15 and 9. What is your mean score?
12 + 15 + 9 = 36
I add up all the values to get the total.
36 ÷ 3 = 12
I divide the total by the number of values: there are 3 scores, so I divide by 3.
Result: The mean of the three scores is 12.
Four friends have 5, 7, 6 and 2 marbles. How many marbles would each get after a fair share?
5 + 7 + 6 + 2 = 20
I pool all the marbles: 20 marbles in total.
20 ÷ 4 = 5
I share fairly among the 4 friends: 5 marbles each. The mean is exactly this fair share.
Result: The mean is 5 marbles per person.