Standard Deviation

How far a typical value sits from the average, in the same units as the data.

Also known as: stddev, std dev, STDEV

The standard deviation says how far a typical value sits from the mean, in the same units as the data itself. If order values average 50 with a standard deviation of 8, a typical order sits roughly 8 away from 50 — not 8 squared, and not 8 percent.

Two different quantities share the name, and they are worth keeping apart:

The population standard deviation, written σ, is the true spread of everything you are describing. You only know it when you have every row of the population.
The sample standard deviation, written s, is your estimate of σ from the rows you happened to measure. It divides the squared deviations by n − 1 instead of n, which makes it slightly larger and, on average, closer to the truth.

So describing every order from last quarter is one job — you have the population, and the population formula is the right one. Estimating the spread of all future orders from 400 of them is a different job, where you only ever have the estimate. Say which one a number is when you report it.

Most tools make you choose explicitly:

import statistics as st
data = [10, 12, 11, 13, 12, 400]
st.pstdev(data)   # population version
st.stdev(data)    # sample version

Spreadsheets keep them as separate functions — STDEV.S for the sample version and STDEV.P for the population version in Excel, with STDEVA and STDEVPA as the variants that treat text as zero. In SQL there is no single default: STDDEV is engine-specific, some engines expose both STDDEV_SAMP and STDDEV_POP, and one of them may be missing entirely. Read your engine’s documentation rather than assuming which you are getting.

The trade-off is that outliers pull the standard deviation around, so one very large value makes a tight column look scattered when it mostly is not. On skewed data the IQR or percentiles describe spread more honestly. When a column is roughly bell-shaped, about two thirds of values sit within one standard deviation of the mean — see the normal distribution for that property and its limits.

For how much an average wobbles when you resample, see standard error.