Standard Deviation Calculator

How do you calculate standard deviation?

Standard deviation measures how spread out numbers are from the mean. The steps are: (1) Find the mean (average), (2) Subtract the mean from each number and square the result, (3) Find the average of those squared differences (divide by n for population, n−1 for sample), (4) Take the square root. This calculator does all steps automatically.

What is the difference between sample and population standard deviation?

Population standard deviation (σ) divides by n (total count) and is used when your data includes every member of the group. Sample standard deviation (s) divides by n−1 (Bessel’s correction) and is used when your data is a subset of a larger population. For most real-world data like surveys or experiments, use sample standard deviation.

What is a good standard deviation?

There is no universal “good” standard deviation — it depends on context. A low standard deviation means data points are clustered close to the mean (consistent data), while a high standard deviation means they are spread out (variable data). Compare it to the mean using the coefficient of variation (CV = std dev ÷ mean × 100%) for a relative measure.

What is variance and how is it related to standard deviation?

Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance. While variance is useful in statistical formulas, standard deviation is more interpretable because it uses the same units as the original data.

How do you find the median of a data set?

Sort all numbers from smallest to largest. If the count is odd, the median is the middle number. If the count is even, the median is the average of the two middle numbers. For example, in {2, 4, 4, 4, 5, 5, 7, 9}, the two middle values are 4 and 5, so the median is 4.5.

What is standard error of the mean (SEM)?

Standard error of the mean (SEM) estimates how far the sample mean is likely to be from the true population mean. It equals the standard deviation divided by the square root of the sample size (SEM = s ÷ √n). Smaller SEM values indicate more precise estimates of the population mean.

Is this standard deviation calculator free and private?

Yes, this calculator is 100% free with no limits. All calculations happen locally in your browser — your data is never uploaded to any server. Your last dataset is saved in your browser’s local storage so you can pick up where you left off.

Can I calculate standard deviation in Excel?

Yes. Use STDEV.S() for sample standard deviation and STDEV.P() for population standard deviation in Excel. For variance, use VAR.S() and VAR.P(). However, this online calculator is faster for quick calculations and provides all descriptive statistics at once without writing formulas.