Mean

The calculation

$$\text{mean} = \frac{\text{sum of the values}}{\text{number of values}}$$

For $6, 7, 7, 9, 11$:

$$\frac{40}{5} = 8$$

What it represents

The mean answers: if the total were shared out evenly, how much would each get? Five students scoring $40$ marks between them average $8$ each.

That is why the mean often is not a value anyone actually has. The mean of $4$ and $7$ is $5.5$, and a mean family size of $2.4$ children describes no family.

Working backwards

Because the mean is the total divided by the count, any two of the three give the third:

$$\text{total} = \text{mean} \times \text{count}$$

Six numbers with a mean of $7$ must total $42$. That is the route into most questions about a missing value or a changing data set.

Its weakness

The mean uses every value, so an extreme one has extreme influence. Seven salaries of $28, 30, 31, 32, 34, 35$ and $350$ thousand have a mean of about $77$ — higher than six of the seven people earn.

That is an outlier at work, and it is why the median is reported for salaries and house prices. See mean, median and mode for how to choose between them.

Pair the mean with mean absolute deviation when reporting spread. Both use every value, so they describe the data the same way.