The mean: add them up, share equally
Eight answers, in minutes: 5, 6, 7, 5, 6, 8, 9, 10. What one number can describe them all?
Step 1 of 4
- One bar for each answer.
- Cut the tops off the tall bars: 1 + 2 + 3 = 6 extra.
- Fill the short bars: 2 + 1 + 2 + 1 = 6 needed.
- Now every bar is 7. The mean is 7.
One number can describe all eight. It is the mean: 7 minutes.
The rule
The mean is the sum divided by the count. It is each value's share when the total is shared equally.
- Sum — all the values added together.
- Count — how many values there are.
- Mean = sum ÷ count.
| What | Working | Answer |
|---|---|---|
| The values | 5, 6, 7, 5, 6, 8, 9, 10 | 8 values |
| The sum | 5 + 6 + 7 + 5 + 6 + 8 + 9 + 10 | 56 |
| The mean | 56 ÷ 8 | 7 |
All 12 answers
The next four answers are 8, 8, 12 and 45. The sum of all 12 is 129 minutes. That is 56 + 8 + 8 + 12 + 45.
- Give each of 12 students 10 minutes: 12 × 10 = 120.
- Then 129 − 120 = 9 minutes are left.
- 9 shared by 12 is 0.75 each.
- So the mean is 10 + 0.75 = 10.75 minutes.
Watch out!
"The mean is 10.75, so most take about 11 minutes." Not quite. 10 of the 12 trips are shorter than 10.75. One 45-minute trip pulls the mean up. Without it, the mean of 11 trips is about 7.6.
Slide the last trip. Watch the mean.
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