Which term is used for variance based on a sample, often denoted by s^2?

Which term is used for variance based on a sample, often denoted by s^2?

• A. Sample variance
• B. Population variance
• C. Standard deviation
• D. Range

Answer: (A)

Variance based on a sample is called the sample variance, and it is denoted by s^2. It measures how spread out the sample values are around the sample mean, using the formula s^2 = sum (x_i − x̄)^2 / (n − 1). The n−1 in the denominator makes this an unbiased estimate of the population variance (sigma^2), which would use the population mean and divide by N. The standard deviation is simply the square root of variance (s is the sample standard deviation, sigma is the population standard deviation). The range, in contrast, is just the difference between the maximum and minimum values and does not represent variance.

Variance based on a sample is called the sample variance, and it is denoted by s^2. It measures how spread out the sample values are around the sample mean, using the formula s^2 = sum (x_i − x̄)^2 / (n − 1). The n−1 in the denominator makes this an unbiased estimate of the population variance (sigma^2), which would use the population mean and divide by N. The standard deviation is simply the square root of variance (s is the sample standard deviation, sigma is the population standard deviation). The range, in contrast, is just the difference between the maximum and minimum values and does not represent variance.