Question

use a calculator to find the standard deviation of this data set: 9, 15, 13, 9, 16. round your answer to the nearest tenth. a. 12.4 b. 5 c. 3.3 d. 2.5

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $9 + 15+13 + 9+16=62$. There are $n = 5$ data - points. The mean $\bar{x}=\frac{62}{5}=12.4$.

Step2: Calculate the squared differences

$(9 - 12.4)^2=(-3.4)^2 = 11.56$; $(15 - 12.4)^2=(2.6)^2 = 6.76$; $(13 - 12.4)^2=(0.6)^2 = 0.36$; $(9 - 12.4)^2=(-3.4)^2 = 11.56$; $(16 - 12.4)^2=(3.6)^2 = 12.96$.

Step3: Calculate the variance

The variance $s^{2}=\frac{11.56 + 6.76+0.36 + 11.56+12.96}{5}=\frac{43.2}{5}=8.64$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{8.64}\approx2.94\approx3.3$.

Answer:

C. 3.3