Which average, when
Most students play a little. A few play for a long time.
- A tall first bar, then a falling tail.
- Its modal class marked.
- Median 12.5 and mean 15 marked, apart.
What a tail does
Here are 60 made-up readings from a rainy Saturday.
| Minutes played | Frequency |
|---|---|
| 0-10 | 25 |
| 10-20 | 20 |
| 20-30 | 8 |
| 30-40 | 4 |
| 40-50 | 3 |
For this table the mean is 15 and the median is 12.5. The modal class is 0-10. The mean and the median differ. The table has a long tail on the right. A tail is a run of high values with small frequencies.
The mean uses every value. A few huge values pull it up far more than the median. The median is the middle value. The mode is the most common value.
The mean adds the size of every reading. The median only needs the middle position. Use the mean when you need a total. Total = mean × number of readings, because the mean is total ÷ number. Use the median for a typical reading when a tail exists. Use the mode for the most common one. For a table with a mild tail, 3 × median = mode + 2 × mean. This rule is only approximate.
Pick the average that answers each question.
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