Question

The variance of a set of numbers (x_1, x_2, ..., x_k) is given by (V = sum (x - barx)^2 / n), where (V) is the variance, ((x - barx)^2) is the square of the deviation from the mean, and (n) is the number of elements in the set. Complete the expression for variance.

a. (V = sum (x - barx))
b. (V = sum (x - barx) / n)
c. (V = sum (x - barx)^2)
d. (V = sum (x - barx)^2 / n^2)

Answer 1

The correct formula for variance is 'd. (V = sum (x - barx)^2 / n)', where n is the number of observations for a population, and n-1 is used if it is a sample to get the sample variance, which is an unbiased estimator of the population variance.

Step-by-step explanation:

The correct expression for variance, based on the information provided, is: d. (V = sum (x - barx)^2 / n). This is because variance is defined as the mean of the squared deviations from the mean (sample mean or population mean). For a population, the variance is calculated by dividing the sum of squared deviations by N, which is the total number of observations in the population. However, for a sample, the variance is computed by dividing the sum of squared deviations by n - 1, which is one less than the number of observations in the sample. This adjustment, using n - 1, provides an unbiased estimator of the population variance, known as the sample variance.