Sample or population standard deviation: which should you select?
The correct denominator depends on whether you are describing the complete group of interest or estimating spread from a sample of a larger group.
Standard deviation →Define the group before calculating
If the data include every member of the group you want to describe, use population mode. If they are a sample used to estimate the variability of a larger population, sample mode commonly uses N−1 in the variance calculation. A small list is not automatically a sample, and a long list is not automatically a population. The research question, not the list length, decides.
Compare the same three values
For 2, 4 and 6, the mean is 4 and the sum of squared deviations is 8. Population variance is 8/3 and standard deviation is about 1.632993. Sample variance is 8/2 = 4 and sample standard deviation is 2. Both outputs can be correct descriptions of the calculation chosen; they are answering different statistical questions.
Keep the inference modest
Sample variance with N−1 has an unbiasedness property under standard independent sampling assumptions; the square-root sample standard deviation is not thereby exactly unbiased. A sample calculation requires at least two observations. Neither setting corrects biased sampling, correlated observations or bad measurements. Record which mode you selected alongside the result so that someone reproducing the work will use the same definition.
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.