Standard deviation measures how spread out a set of values is around their mean, in the same units as the data. A small value means observations cluster tightly; a large one means they scatter widely and any average taken from them is less informative.
σAn average on its own is close to useless. Two products can both average £40 per order — one because almost every order is between £35 and £45, the other because most orders are £12 and a handful are £900. Those are different businesses and they need different decisions, and the standard deviation is the number that tells them apart. It is the typical distance between an observation and the mean, expressed in the same units as the data, which is what makes it readable in a way variance is not.
The reason it appears in every statistical formula is that it drives precision. The standard error of a mean is the standard deviation divided by the square root of the sample size, so a metric with twice the spread needs four times the observations to be measured as precisely. This is why an experiment on conversion rate is comfortable at fifty thousand users and the same experiment on revenue per user is not: revenue is far more variable, and the sample size required scales directly with the variance.
As a rule of thumb for roughly symmetric, bell-shaped data, about 68% of observations fall within one standard deviation of the mean, 95% within two and 99.7% within three. That rule is genuinely useful and genuinely fragile. It comes from the normal distribution, and business metrics are frequently nothing like normal — revenue per user is heavily right-skewed, with a long tail of large purchases — so applying it to skewed data produces confident nonsense such as intervals extending below zero on a quantity that cannot be negative.
Skew also makes the standard deviation itself unstable. Because deviations are squared, a single very large observation moves it far more than it moves the mean, so a metric with a fat tail has a standard deviation that jumps around between samples. That is why revenue experiments so often benefit from winsorising or capping extreme values, or from analysing a log transform: not to hide the outliers but to stop one customer's £40,000 order deciding the precision of the whole analysis.
One technical detail worth getting right: dividing by n − 1 rather than n. Using the sample mean to compute deviations makes them slightly too small, because the sample mean is by construction the point that minimises them, and n − 1 corrects that bias. At n = 1,000 it changes nothing you would notice; at n = 8 it matters, and it is the difference between the two buttons on a spreadsheet that people pick at random.
The square root of the average squared deviation. The n − 1 in the sample version is the only subtle part.
s = √( Σ(xᵢ − x̄)² / (n − 1) )n − 1 corrects for using the sample mean rather than the true one. This is the version you want almost always.
σ = √( Σ(xᵢ − μ)² / N )For when you have every member of the population, which in practice is almost never.
σ = √( p(1 − p) )Determined entirely by the rate, and maximised at p = 0.5. This is why low-conversion metrics need such large samples relative to their mean.
SE = s / √nThe link between spread and precision — see the two-sample t-test calculator, which uses it directly.
Two metrics from the same experiment population of 40,000 users per arm. Conversion runs at 4.0%. Revenue per user averages £6.80 with a standard deviation of £91, driven by a small number of very large orders.
Conversion can be measured to within about 0.1 percentage points — a 2.4% relative precision. Revenue can be measured to within £0.46, which is 6.7% of its own mean.
Same users, same experiment, and revenue is nearly three times harder to measure relative to its size. The coefficient of variation makes the comparison directly: revenue's spread is 13.4 times its mean, conversion's is 4.9 times. Because sample size scales with variance, closing that gap by traffic alone would need roughly seven times the users. The cheaper route is to attack the standard deviation itself — winsorising revenue at the 99th percentile typically cuts it by a third or more here, which is worth about half the sample, and [CUPED](/glossary/cuped) on a pre-period revenue covariate usually does more. Both decisions must be made before looking at results, or they become a way of choosing the answer.
Learn why deviations from normality are often not a significant concern in A/B testing, understand the pros and cons of using the t-test in such scenarios, and explore alternative methods to the traditional t-test.
A/B testing analysts often encounter skewed distributions for different KPIs. Learn why outliers can be problematic, explore the challenges of identifying and handling them, and get practical guidelines for dealing with them effectively.
Applying it to a live measurement problem is the part that goes wrong. If you are designing an experiment, reading a result you do not trust, or trying to work out what your marketing actually caused, that is the work we do.