Question

describe the difference between the calculation of population standard deviation and that of sample standard deviation. let n be the number of data entries in a population and n be the number of data entries in a sample data set. choose the correct answer below. a. when calculating the population standard deviation, the sum of the squared deviation is divided by n, then the square root of the result is taken. when calculating the sample standard deviation, the sum of the squared deviations is divided by n - 1, then the square root of the result is taken. b. when calculating the population standard deviation, the sum of the squared deviation is divided by n. when calculating the sample standard deviation, the sum of the squared deviations is divided by n - 1. c. when calculating the population standard deviation, the sum of the squared deviation is divided by n - 1. when calculating the sample standard deviation, the sum of the squared deviations is divided by n. d. when calculating the population standard deviation, the sum of the squared deviation is divided by the number of entries, n - 1, then the square root of the result is taken. when calculating the sample standard deviation, the sum of the squared deviations is divided by n, then the square root of the result is taken.

Explanation:

The key difference in their calculations lies in the denominator used. Population standard - deviation divides the sum of squared deviations by the population size N, while sample standard - deviation uses n - 1 (Bessel's correction) to account for bias in sample estimates. After dividing, the square root is taken for both to get the standard deviation.

Answer:

A. When calculating the population standard deviation, the sum of the squared deviation is divided by N, then the square root of the result is taken. When calculating the sample standard deviation, the sum of the squared deviations is divided by n - 1, then the square root of the result is taken.