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 deviations 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 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. 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 - 1. d. 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.

Explanation:

The formula for population standard deviation $\sigma=\sqrt{\frac{\sum_{i = 1}^{N}(x_i-\mu)^2}{N}}$, where $N$ is the number of data - points in the population, $x_i$ are the data - points, and $\mu$ is the population mean. The formula for sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$, where $n$ is the number of data - points in the sample and $\bar{x}$ is the sample mean. When calculating the population standard deviation, the sum of the squared deviations is divided by $N$. When calculating the sample standard deviation, the sum of the squared deviations is divided by $n - 1$.

Answer:

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