Measurement of Dispersion

Variance and Standard Deviation

• empirical variance s squared = (1/n) * sum((x - mean(x)) * (x - mean(x)))
• empirical standard deviation s = sqrt((1/n) * sum((x - mean(x)) * (x - mean(x))))
• sample variance = (1/(n-1)) * sum((x - mean(x)) * (x - mean(x)))

Properties of Variance and Standard Deviation

• senstive with respect to outliers
• Variance and standard deviation do not set the dispersion in relation to the location of the data
• With larger (average) values usually also variance and standard deviation are larger

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Coefficient of Variation

• more suitable for dispersion comparison of distributions with very different (average) values
• calculation in R: (sqrt((1/n) * sum((x - mean(x)) * (x - mean(x))))) / mean(x)

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