Standard Deviation

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Example: five people take 4, 6, 7, 8 and 10 minutes to get to work. How much do these times vary around the mean? Change the values to work out your own case.

Values x_i One value per observation, separated by spaces or commas.

Step by step

What each term means

Sample Standard Deviation (s): Measures how far the values spread around the mean, in the same units as the data: the larger it is, the more scattered they are. It is the square root of the variance s².
Summation (Σ): Adds the next term for each of the n values, from i = 1 to i = n.
Squared Deviation ((xᵢ − x̄)²): The distance from each value to the mean x̄, squared. Squaring makes every deviation positive — without it, the deviations would cancel out and always add up to zero — and gives more weight to distant values.
Degrees of Freedom (n − 1): The number of values minus one. Since x̄ was computed from the data themselves, only n − 1 deviations are free: the last one is set by the others. Dividing by n − 1 rather than n corrects the sample's tendency to understate the spread (Bessel's correction).