Standard Deviation Calculator
Calculate mean, median, mode, variance, and standard deviation from a data set.
Paste or type your numbers separated by commas, spaces, or new lines
Use Sample for most practical purposes. Population when you have the entire data set.
How It Works
Parses the input data, calculates the mean (average), then finds each value's deviation from the mean. Squares the deviations, averages them (dividing by n for population or n-1 for sample), giving variance. The square root of variance is the standard deviation. Also identifies median and mode.
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean (average). A low SD means data points cluster close to the mean; a high SD means they are more spread out. It is the square root of the variance.
When should I use sample vs population?
Use population (divide by n) when your data represents the entire group. Use sample (divide by n-1) when your data is a subset — this corrects for the bias of underestimating population variance. In practice, sample is more common.
What is a good standard deviation?
There is no universal 'good' SD — it depends on context. In manufacturing, low SD means consistent quality. In investments, low SD means less volatility. Compare SD relative to the mean using the coefficient of variation (SD/mean x 100%).
What is the difference between variance and standard deviation?
Variance is the average of squared differences from the mean. Standard deviation is the square root of variance. SD is preferred for interpretation because it is in the same units as the original data.
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