Which symbol is commonly used to denote the variance of a sample?

Which symbol is commonly used to denote the variance of a sample?

• A. μ
• B. σ^2
• C. S^2
• D. X̄

Answer: (C)

Notating variance depends on whether you’re talking about the whole population or just a sample. The population variance is written as sigma squared, and the population mean as mu. The sample mean is X-bar, and the variance computed from the sample data is denoted by S^2 (in many texts you’ll also see s^2). S^2 signals a statistic derived from the sample and serves as an estimate of the population variance, using the formula (1/(n−1)) times the sum of (xi − X-bar) squared. Since the question asks for the variance of a sample, the symbol S^2 is the conventional choice.

Notating variance depends on whether you’re talking about the whole population or just a sample. The population variance is written as sigma squared, and the population mean as mu. The sample mean is X-bar, and the variance computed from the sample data is denoted by S^2 (in many texts you’ll also see s^2). S^2 signals a statistic derived from the sample and serves as an estimate of the population variance, using the formula (1/(n−1)) times the sum of (xi − X-bar) squared. Since the question asks for the variance of a sample, the symbol S^2 is the conventional choice.