Question

Find the standard deviation. Round to the nearest tenth. 1, 2, 11, 8, 16, 16,20, 16, 18 OA. 6.5 O B. 6.9 O C. 1.5 ? D. 7.4

Answer 1

Answer:

A. 6.5

Step-by-step explanation:

First we find the average  $\bar{x}$ of the 9 data:

$\bar{x} =\frac{\sum_{x=1}^{n}x_{i}}{n}$

Where n is the data number, that in this case is 9.

$\bar{x} =\frac{1+ 2+ 11+ 8+ 16+ 16+20+ 16+ 18}{9}=12$

The formula of the standard deviation $\sigma$ is:

$\sigma=\sqrt{\frac{\sum_{x=1}^{n}(x_{i}-\bar{x})^{2}}{n}}$

We replace the data and find the value of the standard deviation:

$\sigma=\sqrt{\frac{(1-12)^{2}+(2-12)^{2}+(11-12)^{2}+(8-12)^{2}+(16-12)^{2}+(16-12)^{2}+(20-12)^{2}+(16-12)^{2}+(18-12)^{2}}{9}}$

$\sigma=\sqrt{\frac{(-11)^{2}+(-10)^{2}+(-1)^{2}+(-4)^{2}+(4)^{2}+(4)^{2}+(8)^{2}+(4)^{2}+(6)^{2}}{9}}=6,54$

We approximate the number and the solution is 6,5