Question

calculate standard deviation
a contractor records the areas, in square feet, of several houses in a neighborhood to determine data about the neighborhood. which formula should be used to calculate the standard deviation?

$s^{2}=\frac{(x_1 - overline{x})^{2}+(x_2 - overline{x})^{2}+...+(x_n - overline{x})^{2}}{n - 1}$

$s=sqrt{\frac{(x_1 - overline{x})^{2}+(x_2 - overline{x})^{2}+...+(x_n - overline{x})^{2}}{n - 1}}$

$sigma^{2}=\frac{(x_1 - mu)^{2}+(x_2 - mu)^{2}+...+(x_n - mu)^{2}}{n}$

$sigma=sqrt{\frac{(x_1 - mu)^{2}+(x_2 - mu)^{2}+...+(x_n - mu)^{2}}{n}}$

done

Explanation:

Step1: Identify sample vs population

The contractor records areas of several houses (a sample of the neighborhood), so we use sample - standard deviation formula.

Step2: Recall standard deviation formula

The formula for sample standard deviation is $s=\sqrt{\frac{(x_1 - \bar{x})^2+(x_2 - \bar{x})^2+\cdots+(x_n - \bar{x})^2}{n - 1}}$, where $x_i$ are the data - points, $\bar{x}$ is the sample mean, and $n$ is the sample size.

Answer:

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