The pooled standard deviation is the average spread of all data values about their own mean. it is the weighted average of each group's standard deviation.
where ni is the ith sample size and si is the ith sample standard deviation.
When there are only two samples, the following formula can be used to find the pooled standard deviation.
Group1: (19 21 13 19 16 15 17 17 16 16)
Group2: (13 14 16 15 17 11 13 16 12)
| Group1 | Group2 | |
| n | 10 | 9 |
| x̄ | 16.9 | 14.1111 |
| v | 5.2111 | 4.1111 |
| s | 2.2828 | 2.0276 |
Now the pooled standard deviation will be
or
