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Math & Statistics

Standard Deviation Calculator

Calculate the mean, sample standard deviation, and population standard deviation for a set of 5 numbers.

Inputs

-10,00010,000
-10,00010,000
-10,00010,000
-10,00010,000
-10,00010,000

Calculation Results

Mean (Average)

20

Population Standard Deviation (σ)

7.07

Sample Standard Deviation (s)

7.91

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Formula & Mathematical Explanation

σ=∑(xi−μ)2N,s=∑(xi−xˉ)2n−1\displaystyle \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}, \quad s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}

Population standard deviation (σ) is calculated using N (total number of values) as the divisor, whereas sample standard deviation (s) uses n - 1 (Bessel's correction) to account for sample bias.

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