Question

which of the following is true regarding a sample variance? it is always greater than the population variance. it is exactly the same as the variance of a population. it is always smaller than the population variance. it is an unbiased estimate of the population variance. i dont know one attempt

Explanation:

• Option 1: A sample variance is not always greater than the population variance. It depends on the sample.
• Option 2: A sample variance is not exactly the same as the population variance. The sample is a subset of the population.
• Option 3: A sample variance is not always smaller than the population variance. It depends on the sample.
• Option 4: By definition, the sample variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\) is an unbiased estimate of the population variance \(\sigma^{2}=\frac{\sum_{i = 1}^{N}(x_{i}-\mu)^{2}}{N}\).

Answer:

It is an unbiased estimate of the population variance.