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Chapter 5 · Data Analysis: A Concise Overview of Statistical Techniques · Slide 173/274

Measures of Dispersion

The mean acts like a balance point – the average deviation from the mean is always zero.

5.1.3 · Summarizing Data NumericallyMeasures of Dispersion

Measures of Dispersion

Sample
Variance
s² = ∑(xᵢ − x̄)² / (n − 1)
Why variance?
x̄ = (1.5 + 2.5 + 3.5 − 0.5 + 4.5 + 1.5 − 2.5 − 6.5 + 2.5 − 0.5 − 2.5 − 3.5) / 12 = 0

The mean acts like a balance point – the average deviation from the mean is always zero.

In the variance, all deviations are squared, so that negative and positive deviations do not cancel out.

s² = 117 / (12 − 1) ≈ 10.6
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