Standard deviation of {1, 2, 3, 4, 5}

Subject: Statistics

Standard deviation of {1, 2, 3, 4, 5}

Find the population and sample standard deviations of a uniform data set.

Answer mean = 3, median = 3, mode = no mode (all values unique), σ = 1.41421

Solution

Count & sum n = 5, Σx = 15
Mean x̄ = Σx / n = 15 / 5 = 3
Median middle value of the sorted data = 3
Mode no mode (all values unique)
Range max − min = 5 − 1 = 4
Population variance σ² = Σ(x − x̄)² / n = 2
Population std dev σ = √σ² = 1.41421
Sample variance s² = Σ(x − x̄)² / (n − 1) = 2.5
Sample std dev s = √s² = 1.58114

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