Skip to content
OneKitly
Sign up · Sign in

Population standard deviation calculator

The population standard deviation σ of a data set — how far the values spread from their mean when your data covers the whole group, dividing by N (not n−1). Enter the numbers and it returns σ, the variance σ², the mean and the count.

Related tools

All Statistics & probability tools →
Standard deviation calculatorCompute the standard deviation, variance and mean of a list.Sample Standard Deviation CalculatorCompute the sample standard deviation (n−1), variance, mean and detect outliers.Mean absolute deviation (MAD) calculatorCompute the mean absolute deviation of a data set around its mean.Standard error calculatorCompute the standard error of the mean from a list of numbers.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.Median absolute deviation calculatorA robust measure of spread: the median of the absolute distances from the median. It shrugs off outliers where the standard deviation would blow up. Multiply by 1.4826 to estimate the standard deviation of clean data.Quartile Deviation CalculatorCompute the semi-interquartile range and its coefficient, a spread measure that the extreme values cannot distort.Gini coefficient calculatorThe Gini coefficient of a distribution — the standard measure of inequality, from 0 (everyone equal) to 1 (one person has everything). Paste any set of non-negative values — incomes, wealth, market shares — and it computes the Gini and expresses it as a percentage, the way income inequality is usually reported.

The Population standard deviation calculator turns Data into Population σ, Variance σ², Mean, Count N, instantly and for free. For instance, with Data = 78, 85, 92, 88, 76, 95, 82, 89 it returns Population σ = 6.224, Variance σ² = 38.734 and Mean = 85.625.

How to use it

  1. Enter your values: Data.
  2. Read the result instantly: Population σ, Variance σ², Mean, Count N.

Frequently asked questions

How does the Population standard deviation calculator work?

It takes Data and derives Population σ, Variance σ², Mean and Count N from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

A single value: Data. Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With Data = 78, 85, 92, 88, 76, 95, 82, 89, the calculator returns Population σ = 6.224, Variance σ² = 38.734 and Mean = 85.625. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using Data = 78, 89, 101, 101, 91, 119, 107, 120 instead, Population σ goes from 6.224 to 13.663 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Data = 78, 85, 92, 88, Population σ comes out at 5.117. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

What is the difference between the Population standard deviation calculator and the Standard deviation calculator?

This one returns Population σ and Variance σ²; the Standard deviation calculator returns Std. deviation (σ) and Variance. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Sample Standard Deviation Calculator is the closest one after this: Compute the sample standard deviation (n−1), variance, mean and detect outliers.

What else is worth having open alongside it?

Mean absolute deviation (MAD) calculator and Standard error calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerWhat Is a Percentile? The 90th Percentile ExplainedA percentile tells you where a value ranks within a group. Learn what the 90th percentile really means and why a percentile is not the same as a percentage.How-toHow to Calculate a Weighted AverageA weighted average gives some values more influence than others. Learn the Σ(w·x) / Σw formula with grade and portfolio examples you can follow step by step.How-toScientific Notation ExplainedScientific notation writes huge and tiny numbers as a value times a power of ten. Here's how to write it, read the exponent, and convert back.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.