One unusual value can transform your standard deviation
Squared deviations give distant values a strong influence. Investigate unusual observations before deciding what they mean or whether to remove them.
Standard deviation →See the effect numerically
The population data 4, 4, 4 and 4 have mean 4 and standard deviation 0. Replace the last observation with 12: the mean becomes 6, the squared deviations sum to 48, population variance is 12, and standard deviation is √12, about 3.464102. Three values did not change, yet the summary changed substantially because the fourth moved far away.
Check data quality before deletion
An unusual value might be a typing error, a different unit, an instrument fault or a genuine rare event. Return to the original record and document any correction. Removing a valid observation merely because it increases the standard deviation can distort the conclusion. If a rule for exclusion is needed, define it transparently for the study rather than inventing one after seeing an inconvenient result.
Report more than one summary
Use the average tool to inspect the mean and median alongside standard deviation and the raw values. In 4, 4, 4, 12, the median remains 4 while the mean is 6. This difference is informative, but does not prove an error. A standard deviation alone also cannot establish statistical significance or a confidence interval; those require a defined model and additional information about sampling.
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.