Standard Deviation
Standard deviation is a measure of dispersion or variation amongst data.
Instead of taking absolute deviation from the arithmetic mean, we may square each deviation and obtain the arithmetic mean of squared deviations. This gives us the ‘variance’ of the values.
The positive square root of the variance is called the ‘standard deviation’ of the given values.
Standard Deviation for Raw Data
Suppose x1, x2, . . . xn are n values of the x, their arithmetic mean is:
Standard Deviation for Grouped Data
Calculation for standard deviation for grouped data can be shown by this example:
Variance
The square of standard deviation (σ) is called as the variance (σ²).
So if σ = 10, then variance = σ² = 100.
Alternatively, if variance = σ² = 100, then standard deviation = √Variance = √100 = 10.
The larger the standard deviation, the larger the variance.
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