In the variance formula, what does S^2 denote?

In the variance formula, what does S^2 denote?

• A. S^2
• B. X-bar
• C. n
• D. S

Answer: (A)

S^2 represents the variance of the data from a sample. It measures how spread out the data are around the sample mean. Specifically, it is computed as (1/(n-1)) times the sum of squared deviations from the sample mean, where n is the number of observations. The n−1 in the denominator makes this an unbiased estimator of the true population variance when the data come from a random sample. Since the standard deviation is the square root of the variance, the sample standard deviation is S, and S^2 is simply the square of that value. In contrast, the population variance is denoted by σ^2 and uses the population mean μ.

S^2 represents the variance of the data from a sample. It measures how spread out the data are around the sample mean. Specifically, it is computed as (1/(n-1)) times the sum of squared deviations from the sample mean, where n is the number of observations. The n−1 in the denominator makes this an unbiased estimator of the true population variance when the data come from a random sample. Since the standard deviation is the square root of the variance, the sample standard deviation is S, and S^2 is simply the square of that value. In contrast, the population variance is denoted by σ^2 and uses the population mean μ.