Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Population and sample standard deviation use slightly different formulas on purpose, and picking the wrong one systematically understates the spread. Sample deviation divides by one less than the count specifically because a sample tends to underestimate the true variation in the full population it's drawn from, and that adjustment corrects for it.
Before you rely on it
What to check
Decide first whether your six values are the entire population you care about or a sample drawn from something larger. That choice determines which of the two formulas applies.
The common error
Where people go wrong with standard deviation calculator
Defaulting to population deviation out of habit regardless of which situation actually applies. On a genuine sample, that choice understates the real variability, sometimes by a meaningful margin.
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Value 1 | 12 |
| Value 2 | 18 |
| Value 3 | 9 |
| Value 4 | 22 |
| Value 5 | 15 |
| Value 6 | 20 |
| Population standard deviation | 4.5 |
| Sample standard deviation | 4.9 |
Where the inputs come from
Enter the values in your list. Decide whether the data is the whole population or a sample from a larger group. For a population, divide the sum of squared deviations by n, and for a sample, divide by n minus 1, which corrects the tendency of a sample to understate variability. Most real data are samples, so the sample standard deviation is usually the right choice. Check the values for typing errors.
When the result stops applying
Standard deviation is sensitive to outliers, and it can mislead for skewed data or very small samples. It is not a measure of error unless the data are repeated measurements of one quantity. Population and sample versions differ noticeably when n is small. Units matter: the value is in the same units as the data.
What to compare it with
See the mean and median calculator for the center, the range calculator for a simple spread, and the z-score page to place a value relative to the mean. The confidence interval and sample size calculators use it for estimation. Investment volatility on the investing pages is a standard deviation.
People also ask
Frequently asked questions
What is the difference between population and sample standard deviation?
The population version divides by n, and the sample version divides by n minus 1 to correct for estimating the mean from the same data.
What does a large standard deviation mean?
The values are spread far from the mean, so the data is more variable and the mean is a less reliable summary of a typical value.
How is standard deviation used in investing?
As a measure of volatility: the higher the standard deviation of returns, the more the investment's value swings.