The daily temperatures (in degrees Celsius) for a week are 20, 22, 24, 26, 28, 30, and 32. What is the population variance of these temperatures?
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Correct answer
A. 16
Principle or equation
Population variance is the average of the squared deviations from the mean: σ^2 = (1/N) Σ (x_i - μ)^2.
Why this answer is correct
Mean μ = (20+22+24+26+28+30+32)/7 = 182/7 = 26. Deviations: -6, -4, -2, 0, 2, 4, 6. Squares: 36, 16, 4, 0, 4, 16, 36. Sum = 112. Variance = 112/7 = 16.
Example
For data 2, 4, 6, mean = 4, variance = ((4+0+4)/3)=8/3≈2.67.
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