Standard Deviation Calculator
Calculate mean, variance and standard deviation (population and sample) of a data set instantly.
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How Is Standard Deviation Calculated?
Standard deviation measures how spread out values are around the mean. Steps: find the mean, square each value's distance from it, average those squares (the variance), and take the square root. The population formula divides by n; the sample formula divides by n−1 to correct for estimating from a subset — use it when your data is a sample of a larger group.
Paste your numbers separated by commas, spaces or new lines; the tool shows count, mean, min/max, both variances and both standard deviations.
Frequently Asked Questions
Population or sample — which should I use?
If your data covers the entire group of interest (all students in the class), use population (÷n). If it is a subset used to estimate a larger group (a survey), use sample (÷n−1), which gives a slightly larger, unbiased estimate.
What does a standard deviation of 5 mean?
Typical values lie within about ±5 of the mean. For roughly normal data, ~68% of values fall within one standard deviation and ~95% within two.
What is the difference between variance and standard deviation?
Variance is the average squared distance from the mean (units squared); standard deviation is its square root, expressed in the same unit as the data — which is why it is easier to interpret.
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Standard Deviation Calculator