Question

Find the mean, variance, and standard deviation for the data set.7, 13, 8, 3, 11, 7, 14, 7, 18, 2The mean is x =(Round to two decimal places as needed.)The variance is 3 =$0(Round to two decimal places as needed.)The standard deviation is on(Round to two decimal places as needed.)

Answer 1

SOLUTION

Step1; Write out the set of data

7, 13, 8, 3, 11, 7, 14, 7, 18, 2

The mean is given as

$\bar{x}=\frac{\text{SUM OF DATA}}{frequency}$$\bar{x}=\frac{2+3+7+7+7+8+11+13+14+18}{10}=\frac{90}{10}=9$

The mean is 9.00

The variance of a set of data is given as

$\sigma^2=\frac{\sum (x-\bar{x})^2}{n}$

consider the table below

$\begin{gathered} \frac{\sigma^2=(2-9)^2+(3-9)^2+(7-9)^2+(7-9)^2+(7-9)^2+(8-9)^2+(11-9)^2+(13-9)+(14-9)^2+(18-9)^2}{10} \\ \end{gathered}$

Hence the variance becomes

$\sigma^2=\frac{49+36+4+4+4+1+4+16+25+81}{10}_{}$$\sigma^2=\frac{224}{10}=22.40$

The variance is 22.40

The standard deviation is given as

$\begin{gathered} \text{std}=\sqrt[]{variance} \\ \sigma=\sqrt[]{22.40}=4.73 \end{gathered}$