How is variance calculated for a sample set?

The correct calculation of variance for a sample set is provided in the selected choice. When calculating sample variance, the formula is designed to provide an unbiased estimate of the population variance based on a finite sample drawn from that population.

In this context, the variance is represented mathematically as the sum of the squared differences between each data point and the sample mean, divided by the number of observations in the sample minus one. The "- 1" in the denominator, known as Bessel's correction, is crucial because it corrects the bias that occurs when estimating the population variance from a sample. It ensures that the sample variance is an unbiased estimator of the true population variance.

This approach contrasts with the population variance, where the denominator would simply be the total number of observations in the dataset. This subtlety is important for ensuring that the variance calculated from a sample is reflective of the larger population from which the sample is drawn.

The other choices describe various mathematical expressions that do not accurately represent the calculation of sample variance. For instance, one option simply divides by N (the number of items), which would apply to population variance rather than sample variance. Another option appears to describe a normalized value rather than a measure of variance. Thus, it's essential to recognize the