Spread of the integers one through five

Question

What is the standard deviation of the five values $1,2,3,4,5$ ?

Short answer

$\sqrt2\approx1.41$ (population) or $\sqrt{2.5}\approx1.58$ (sample). The mean is $3$ and the squared deviations are $4,1,0,1,4$ , summing to $10$ . Dividing by $5$ gives variance $2$ ; dividing by $n-1=4$ gives $2.5$ .

Adapted from Crack, Heard on the Street, Q4.20, p.41; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Covariance and Correlation
Populations, Samples, and Sampling Distributions

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