Standard deviation measures how spread out values are from the mean. A low standard deviation means values are close to average, while a high standard deviation means values vary widely.
Why Standard Deviation Matters
It is used in:
- Exam score analysis
- Business and quality control
- Investment risk measurement
- Scientific data analysis
Formula (Population)
sigma = sqrt(sum((x - mu)^2) / N)
Where mu is mean and N is number of values.
For samples, divide by n - 1 instead of n.
Simple Example
Dataset: 8, 10, 12, 10
- Mean = (8 + 10 + 12 + 10) / 4 = 10
- Deviations from mean: -2, 0, 2, 0
- Squared deviations: 4, 0, 4, 0
- Average squared deviation = (4 + 0 + 4 + 0) / 4 = 2
- Standard deviation = sqrt(2) = 1.41
How to Interpret It
Standard deviation has the same unit as the original data, making interpretation practical. Always compare it with the mean for better context.
Use Our Standard Deviation Calculator
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