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

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

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

Answer

Brief Explanations:

The standard - deviation formula for sample data uses the sample mean $\bar{x}$ and divides by $n - 1$ (Bessel's correction), where $n$ is the sample size. The first option shows the correct formula for the sample standard deviation. The second and third options use the population mean $\mu$ and divide by $N$ (for population variance and standard - deviation respectively), and the fourth option is missing the square - root operation for the sample standard deviation.

Answer:

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