Question

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

Explanation:

Step1: Recall sample standard - deviation formula

The formula for the standard deviation $s$ of a sample data set $x_1,x_2,\cdots,x_n$ with sample mean $\bar{x}$ is $s = \sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$.

Step2: Analyze the 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 standard deviation of sample data. The second and third options use the population mean $\mu$ and denominator $N$ which are for population standard - deviation. The fourth option is missing the square - root sign.

Answer:

The first option $s=\sqrt{\frac{(x_1-\bar{x})^2+(x_2 - \bar{x})^2+\cdots+(x_n-\bar{x})^2}{n - 1}}$