Which of the following symbols identifies the sample variance?

• A. ${\sigma }^2$
• B. $\sigma$
• C. $s^2$
• D. $s$

Answer: (C)

Verified step by step guidance

1. Understand the difference between population parameters and sample statistics. Population parameters describe the entire population, while sample statistics describe a subset (sample) of the population.
2. Recall that the symbol \(\sigma^2\) represents the population variance, which measures the variability of the entire population data.
3. Recognize that the symbol \(\sigma\) (without the square) represents the population standard deviation, which is the square root of the population variance.
4. Identify that the symbol \(s^2\) represents the sample variance, which estimates the variance based on sample data and is calculated using the formula \(s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2\), where \(n\) is the sample size and \(\bar{x}\) is the sample mean.
5. Note that the symbol \(s\) (without the square) represents the sample standard deviation, which is the square root of the sample variance.