What is the population standard deviation of 2,4,4,4,5,5,7,9?

μ = (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8
μ = 40 / 8
μ = 5

For each data point (x), subtract the mean (μ) and square the result (x - μ)². Then sum these squared differences and divide by the total number of data points (N).

• (2 - 5)² = (-3)² = 9
• (4 - 5)² = (-1)² = 1
• (4 - 5)² = (-1)² = 1
• (4 - 5)² = (-1)² = 1
• (5 - 5)² = (0)² = 0
• (5 - 5)² = (0)² = 0
• (7 - 5)² = (2)² = 4
• (9 - 5)² = (4)² = 16

Sum of squared differences = 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32

Variance (σ²) = Sum of squared differences / N
σ² = 32 / 8
σ² = 4

The population standard deviation is the square root of the variance.

σ = √σ²
σ = √4
σ = 2