Standard Deviation
For a data set containing n measurements the standard deviation, s, is defined as
where xi is the value of an individual measurement and x is the average value of the measurements. The standard deviation is a measure of the precision of the measurements. If s is small the measurements are tightly clustered around the average, and the precision is high. If s large the individual measurements exhibit a wide range of values and the precision is low.
Example. Estimate the standard deviation for the following data:
4.28, 4.21, 4.30, 4.36, 4.26, 4.33
The average value (x) is 4.29.
| xi - x | (xi - x)2 | |
| 4.28 | -0.01 | 0.0001 |
| 4.21 | -0.08 | 0.0064 |
| 4.30 | 0.01 | 0.0001 |
| 4.36 | 0.07 | 0.0049 |
| 4.26 | -0.03 | 0.0009 |
| 4.33 | 0.04 | 0.0016 |
and s = 