📐 Math
Standard Deviation Calculator
Calculate the standard deviation and variance of a dataset. These metrics measure the amount of variation or dispersion from the average (mean). Automatically supports both sample and population calculations.
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Formula
s = √( Σ(x-μ)² / (N-1) )s- Sample standard deviation
x- Each individual value in the data set
μ- The mean of the data set
N- The total number of data points
Example
Calculating Sample Standard Deviation
Calculate for the dataset: 10, 12, 23, 23, 16, 23, 21, 16.
- Calculate the mean (μ): 144 / 8 = 18.
- Find squared deviations from the mean: (10-18)²=64, (12-18)²=36, etc.
- Sum all squared deviations: 64 + 36 + 25 + 25 + 4 + 25 + 9 + 4 = 192.
- Divide by N-1 (which is 8-1=7) to get variance: 192 / 7 ≈ 27.428.
- Take the square root of the variance: √27.428 ≈ 5.237.
- Result: 5.237
Frequently Asked Questions
Use 'Population' if your dataset includes every single member of the group you are studying. Use 'Sample' if your dataset is a representative subset of a larger group, as it uses N-1 to provide an unbiased estimate of the population standard deviation.