Share the pile out equally, and what each one receives is the mean. That is why the formula is the total divided by how many there are.
\[ \text{Mean} = \frac{\text{sum of all the values}}{\text{how many values}} \]
The mean need not be a real value
No family has 2.25 children and none ever will. The mean is a summary of the whole group, not a description of any single member.
Five workers earning 10000, 11000, 12000, 11000 and 96000 have a mean of 28000, which is more than four of them actually earn.
Median and mode
| Average | What it is | When it is the better choice |
|---|---|---|
| Mean | Total shared out equally | When the values are fairly close together |
| Median | The middle value once they are in order | When one or two values are extreme |
| Mode | The value that appears most often | For categories, such as the commonest shoe size |
For those five wages the median is 11000, which describes the group far better. Neither number is wrong; they answer different questions.
Put the values in order FIRST. With an even number of values, take the mean of the two middle ones.
If ten students have a mean of 62, the total must be 620. Recovering the total is the key to almost every backwards question.
A class of 20 with mean 60 and a class of 40 with mean 75 give a combined mean of 70, not 67.5. Go back to the totals.
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Find the mean, median and mode of 8, 6, 9, 5, 7, 6 and 8.
Nine students have a mean mark of 64. A tenth student scores 46.
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The mean is the total shared out equally among all the values.
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