Calculating the mean from a frequency table

x ƒx
1
2
3
4
5
6
7
140
180
60
100
60
40
20
total 600

The mean can be easily calculated from this table:

More generally,

where the summation is over the distinct values in the data set, rather than all individuals.

Calculating the standard deviation

A similar formula holds for the standard deviation, using the formula