What is the average squared deviation from the mean?

What is the average squared deviation from the mean?

• A. Variance
• B. Sum of Squares
• C. Standard Deviation
• D. Range

Answer: (A)

The average squared deviation from the mean is the variance. It measures how spread out the data are around the mean by averaging the squared distances (xi − μ)². For a population, variance is (1/n) ∑(xi − μ)²; for a sample, we use (1/(n−1)) ∑(xi − x̄)². The other options don’t fit this description: the sum of squares is the total of squared deviations without averaging, the standard deviation is the square root of the variance, and the range is the difference between the maximum and minimum values.

The average squared deviation from the mean is the variance. It measures how spread out the data are around the mean by averaging the squared distances (xi − μ)². For a population, variance is (1/n) ∑(xi − μ)²; for a sample, we use (1/(n−1)) ∑(xi − x̄)². The other options don’t fit this description: the sum of squares is the total of squared deviations without averaging, the standard deviation is the square root of the variance, and the range is the difference between the maximum and minimum values.