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ALTREPO/Calculators/STANDARD DEVIATION CALCULATOR: STEP

Standard Deviation Calculator: Step-by-Step Stats

Paste or type your numbers to get the sample and population standard deviation, the variance, the mean, and a clear step by step of the math. Everything runs locally in your browser.

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Standard Deviation Bell Curve A graphic illustrating the 68-95-99.7 rule on a normal distribution curve. μ +1σ -1σ 68%
Standard deviation (σ) measures the spread of your data.
In a normal distribution, about 68% of values fall within one standard deviation of the mean (μ).

How this calculator works

  1. It finds the mean (average) of the numbers you enter.
  2. For each value it measures how far it sits from the mean, then squares that distance.
  3. It adds up those squared distances and divides to get the variance: by the count for a population, or by the count minus 1 for a sample.
  4. Taking the square root brings it back to the same units as your data, giving the standard deviation for both the sample and the population.

Example: for 4, 8, 6, 5, 3, 7 the mean is 5.5. The sample standard deviation is about 1.87 and the population standard deviation is about 1.71.

Standard deviation calculator FAQ

What is standard deviation?

Standard deviation is a measure of how spread out a set of numbers is around their average. A low standard deviation means the values sit close to the mean, while a high one means they are spread over a wider range. It is shown in the same units as your data, which makes it easy to interpret.

Should I use sample or population standard deviation?

Use the sample formula when your data is a subset of a larger group you want to generalize to, and use the population formula when your data is the entire group you care about. The sample formula divides by n minus 1 and returns a slightly larger value to account for the uncertainty of sampling.

How do you calculate standard deviation by hand?

First find the mean of your numbers. Then subtract the mean from each value and square the result. Add up those squared differences, divide by n for a population or by n minus 1 for a sample, and finally take the square root of that result to get the standard deviation.

What is the difference between standard deviation and variance?

The variance is the average of the squared differences from the mean, and the standard deviation is the square root of the variance. Standard deviation is usually easier to interpret because it is expressed in the same units as the original data rather than squared units.

How do I calculate standard deviation in Excel or Google Sheets?

Use STDEV.S for a sample and STDEV.P for a population. Put your numbers in a column, then enter the formula referencing that range, for example STDEV.S(A1:A20), and the spreadsheet returns the standard deviation. The older STDEV function behaves like STDEV.S.