Standard Deviation Formula
Also known as: Population Standard Deviation, SD Formula
\sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N}}
σ = √(Σ(xi - μ)² / N)What It Calculates
Measures how spread out data points are from the mean. A low SD means data is clustered close to the mean; a high SD means data is spread out.
variables
| Symbol | Name | Description |
|---|---|---|
| \sigma | Standard Deviation | Measure of spread in the data |
| x_i | Data Point | Each individual value in the dataset |
| \mu | Mean | Average of all data points |
| N | Count | Total number of data points |
Worked Examples
1
Mean = 40/8 = 52
Deviations: -3,-1,-1,-1,0,0,2,43
Squared: 9,1,1,1,0,0,4,164
Variance = 32/8 = 45
SD = √4 = 2Result: σ = 2
Common Mistakes
Population SD divides by N, sample SD divides by N-1
SD is always non-negative
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