Standard Deviation Calculator
Calculate the standard deviation and variance of a data set, as a sample or a whole population.
Standard deviation (s)
2.138089935
- Variance
- 4.571428571
- Mean
- 5
- Count
- 8
- Sum of squares
- 32
- Standard error of the mean
- 0.755928946
Show the work
Mean
x̄ = Σx ÷ n
40 ÷ 8 = 5
Square each value's distance from the mean and add them
Σ(x − x̄) to the power of 2
(2 − 5) to the power of 2 + (4 − 5) to the power of 2 + (4 − 5) to the power of 2 + (4 − 5) to the power of 2 + (5 − 5) to the power of 2 + (5 − 5) to the power of 2 + (7 − 5) to the power of 2 + (9 − 5) to the power of 2 = 32
Variance: divide by n − 1 (a sample)
s to the power of 2 = Σ(x − x̄) to the power of 2 ÷ (n − 1)
32 ÷ 7 = 4.571428571
Standard deviation: the square root of the variance
s = √s to the power of 2
√4.571428571 = 2.138089935
How it works
s = √(Σ(x − mean)² ÷ (n − 1)) for a sample · σ = √(Σ(x − mean)² ÷ n) for a population
Questions
- How does the standard deviation calculator work?
- s = √(Σ(x − mean)² ÷ (n − 1)) for a sample · σ = √(Σ(x − mean)² ÷ n) for a population.
- What do I need to enter?
- Numbers, Data is a. Optional fields can be left blank.
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