What does a standard deviation of 2 actually mean?
Standard deviation describes spread around a mean, in the original measurement unit. It is not a universal score of good or bad performance.
Standard deviation →Return the variance to useful units
For the full dataset 8, 10 and 12, the mean is 10. Population variance is 8/3, about 2.666667, and population standard deviation is about 1.632993. If the observations are seconds, variance is in seconds squared and standard deviation is in seconds. The square root brings spread back to a unit you can compare with an actual observation.
Separate location from spread
Add 100 to every observation: 108, 110 and 112 now have mean 110 but the same standard deviation. Multiply every observation by 10 instead and the standard deviation multiplies by 10. This explains why changing from metres to centimetres changes the displayed number without changing the physical variability. Compare values only after harmonizing units and measurement procedures.
Do not assume a normal curve
Statements about roughly 68% of observations lying within one standard deviation apply to a normal distribution, not every dataset. A skewed or multimodal set can behave very differently. Check the individual values and a suitable plot before interpreting the spread. Whether a given standard deviation is acceptable depends on tolerances, purpose and the scale of the problem; the calculator cannot set those criteria.
Try the calculators
- Standard deviation
Calculate population or sample standard deviation.
- Average & median
Find the mean, median and sum of a list.
- Scientific calculator
Arithmetic, powers, trigonometry and logarithms.