Definition
Variance is the average squared deviation of values from the mean; the standard deviation (SD) is its square root and has the same units as the data. Both describe how widely values scatter around the mean — a small SD means homogeneous data, a large SD big differences between units.
Foundations & hypothesis testing
The standard deviation is easier to read than the variance because it lives in the original units: "average length 50 mm ± 2 mm". For a normal distribution roughly 68 % of values fall within one SD of the mean and 95 % within two — which is why SD underlies control limits and confidence intervals.
Distinguish the sample standard deviation (divides by n − 1, an estimate for the population) from the standard error of the mean (SD divided by the square root of n), which describes the precision of the mean, not the spread of the data. Mixing them up is one of the most common reporting mistakes.
In Statistica
Descriptive statistics in Statistics → Basic Statistics/Tables return variance, standard deviation, standard error and coefficient of variation; a box plot or histogram from the Graphs menu shows the spread visually. The quality-control modules convert SD into control limits and capability indices.
Related terms
- Mean, median and modeThe mean, median and mode are measures of central tendency — a single number summarizing where the data lie.
- Normal distributionThe normal (Gaussian) distribution is a symmetric bell-shaped distribution described by its mean and standard deviation.
- Confidence intervalA confidence interval is a range of values that, with a stated confidence (most often 95 %), covers the true value of a…
- Process capability (Cp, Cpk)Capability indices compare process variability with the customer's tolerance limits.
Knowledgebase guides
FAQ
- What is the difference between SD and standard error?
- SD describes the spread of individual values; the standard error describes the precision of the estimated mean. The standard error is always smaller and shrinks as the sample grows.
- What is the coefficient of variation?
- SD divided by the mean, usually in percent. It lets you compare the variability of quantities with different units or levels.
Try it on your own data
Statistica free for 30 days
Full version, no credit card. Or get a pricing estimate in a minute.
Foundations & hypothesis testing
Updated: September 2026.