Question

Which of the following sample distributions would be a better representation of a population with a variability of 15.22?

Sample A, variance = 32.40
Sample B, variance = 44.10
Sample C, variance = 18.60"

Answer 1

Sample C would be a better representation of a population with a variability of 15.22 because its variance of 18.60 is closest to the population variance, which is essentially the square of the given variability (15.22² = 231.6484).

Step-by-step explanation:

The question pertains to which sample distribution would better represent a population with a variability of 15.22. Variability in this context likely refers to the standard deviation or variance of the population. The variance of a dataset is a measure of its spread or dispersion.

Since the population variability given is 15.22, this would be the population's standard deviation. To compare it to the sample distributions, we need to square this value to obtain the population variance (since variance is the square of the standard deviation). Hence, the population variance is 15.22² = 231.6484.

Given the sample variances: Sample A with a variance of 32.40, Sample B with a variance of 44.10, and Sample C with a variance of 18.60, Sample C with a variance of 18.60 is closest to the population variance and therefore, would be the better representation of the population's variability.