What is the population standard deviation (σ) for this set of data? 3.76, 4.12, 3.29, 2.84, 4.93, 2.15
A) .98
B) 3.52
C) .80
D) .89

Question

Quizplus · Accepted Answer

The population standard deviation (σ) is calculated by taking the square root of the variance. The variance is the average of the squared differences from the Mean. For this data set: Mean (μ) = (3.76 + 4.12 + 3.29 + 2.84 + 4.93 + 2.15) / 6 = 21.09 / 6 = 3.515. Then, for each number, subtract the Mean and square the result, then average those squared differences. Variance (σ^2) = [(3.76-3.515)^2 + (4.12-3.515)^2 + (3.29-3.515)^2 + (2.84-3.515)^2 + (4.93-3.515)^2 + (2.15-3.515)^2] / 6 = 0.792025. Finally, take the square root of the variance to get the standard deviation: σ = sqrt(0.792025) ≈ 0.89.

What Is the Population Standard Deviation (σ) for This Set