estimate of the mean

When discrete data or continuous data are grouped in a frequency table, it’s impossible to calculate the exact mean. Nevertheless, we can calculate an estimate of the mean by using the middle value.

Let’s use the example opposite.

The data shows the duration of telephone calls from an office over a one-week period.

The first colum shows the duration of the telephone calls; the class interval is 5. The frequency of these calls can be seen in the second column. The third column shows the middle value of the duration of the calls.

In order to calculate the fx value of each group, we multiply the frequency (f) by the middle value (x).

Then, we calculate the total of the f column and the total of the fx column.

Lastly, we divide the fx total by the f total in order to get an estimate of the mean.

Therefore, in this example, the estimate of the mean is 2730 ÷ 300 = 9.1 minutes or 9 minutes and 11 seconds.