Calculate the mean, variance and standard deviation of a data set by entering numbers separated by commas or spaces.
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Standard deviation measures how spread out a set of numbers is from the mean. It's calculated by finding the mean, then the squared difference of each number from that mean (called variance), then taking the square root of the variance.
This calculator computes population standard deviation, dividing by the total count of numbers. Sample standard deviation (used when your data is a sample of a larger population) divides by count minus one instead, resulting in a slightly larger value.
For the data set 4, 8, 15, 16, 23, 42 (6 numbers): the mean is (4+8+15+16+23+42) ÷ 6 = 108 ÷ 6 = 18. The squared differences from the mean are (4−18)²=196, (8−18)²=100, (15−18)²=9, (16−18)²=4, (23−18)²=25, and (42−18)²=576. Their sum is 910, and dividing by the count of 6 gives a population variance of 151.6667. The standard deviation is the square root of that: √151.6667 ≈ 12.3153.
Assuming this calculator's result is sample standard deviation, it computes the population version (dividing by count), which is slightly smaller than the sample version (dividing by count minus one); use the Statistics Calculator if you need both figures side by side.
Confusing variance with standard deviation, variance is the squared-difference average and is in squared units, while standard deviation (its square root) is back in the original units and easier to interpret directly.
Entering only one number, standard deviation measures spread across multiple values, so this calculator requires at least two numbers to produce a meaningful result.
A low standard deviation means the numbers are clustered closely around the mean, while a high standard deviation means they're spread out over a wider range.
Enter numbers separated by commas, spaces, or both, for example '4, 8, 15, 16, 23, 42' or '4 8 15 16 23 42' both work.
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