Free tool
Statistics Calculator
Paste or type your numbers to instantly get the mean, median, mode, range, variance, and standard deviation - both sample and population. It runs in your browser and saves nothing.
Enter at least one number to see the mean, median, mode, range, variance, and standard deviation.
How to calculate standard deviation (worked example)
Standard deviation measures how spread out your numbers are around the mean. The sample formula is:
s = √( Σ(x − x̄)² / (n − 1) )
Take the data set 4, 8, 6, 5, 3, 7:
- Mean: (4 + 8 + 6 + 5 + 3 + 7) / 6 = 33 / 6 = 5.5.
- Squared differences from the mean: 2.25, 6.25, 0.25, 0.25, 6.25, 2.25 - which add up to 17.5.
- Sample variance: 17.5 / (6 − 1) = 17.5 / 5 = 3.5.
- Sample standard deviation: √3.5 ≈ 1.87. (For the population version, divide by 6 instead of 5, giving √2.9167 ≈ 1.71.)
Frequently asked questions
How do you calculate standard deviation?+
Find the mean of your data, subtract the mean from each value and square the result, add those squared differences, divide by n - 1 for a sample (or by N for a population), then take the square root. For 4, 8, 6, 5, 3, 7 the mean is 5.5, the squared differences add to 17.5, so the sample standard deviation is the square root of 17.5 / 5, about 1.87. This calculator does all of that as you type.
What is the difference between sample and population standard deviation?+
Sample standard deviation divides by n - 1 (Bessel's correction) and is used when your data is a sample drawn from a larger group - this is the one most stats classes and calculators default to. Population standard deviation divides by N and is used only when your data is the entire group. The calculator shows both so you can pick the right one.
What is the difference between mean, median, and mode?+
The mean is the arithmetic average (sum divided by count). The median is the middle value when the data is sorted. The mode is the value that appears most often. The mean is sensitive to outliers; the median is not, which is why skewed data is often described by its median.
Is this statistics calculator free?+
Yes - it's completely free, runs entirely in your browser, and stores nothing. Paste your numbers to see the mean, median, mode, range, variance, and standard deviation instantly.
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