which formula is used to calculate the standard deviation of sample data?\ns = sqrt{\frac{(x_1-overline{x})^2…

which formula is used to calculate the standard deviation of sample data?\ns = sqrt{\frac{(x_1-overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n-overline{x})^2}{n - 1}}\n sigma^2=\frac{(x_1-mu)^2+(x_2-mu)^2+cdots+(x_n-mu)^2}{n}\n sigma=sqrt{\frac{(x_1-mu)^2+(x_2-mu)^2+cdots+(x_n-mu)^2}{n}}\ns=\frac{(x_1-overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n-overline{x})^2}{n - 1}

which formula is used to calculate the standard deviation of sample data?\ns = sqrt{\frac{(x_1-overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n-overline{x})^2}{n - 1}}\n sigma^2=\frac{(x_1-mu)^2+(x_2-mu)^2+cdots+(x_n-mu)^2}{n}\n sigma=sqrt{\frac{(x_1-mu)^2+(x_2-mu)^2+cdots+(x_n-mu)^2}{n}}\ns=\frac{(x_1-overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n-overline{x})^2}{n - 1}

Answer

Explanation:

Step1: Recall sample standard - deviation formula

The formula for the standard deviation of a sample is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the sample data points, $\bar{x}$ is the sample mean, and $n$ is the sample size.

Step2: Analyze given options

The first option $s=\sqrt{\frac{(x_{1}-\bar{x})^{2}+(x_{2}-\bar{x})^{2}+\cdots+(x_{n}-\bar{x})^{2}}{n - 1}}$ is the correct formula for the sample standard deviation. The second and third options use the population mean $\mu$ and the population size $N$, which are for population variance and standard - deviation. The fourth option is missing the square - root sign.

Answer:

The first option $s=\sqrt{\frac{(x_{1}-\bar{x})^{2}+(x_{2}-\bar{x})^{2}+\cdots+(x_{n}-\bar{x})^{2}}{n - 1}}$