Question

Variance and Standard DeviationFind the variance and the standard deviation of the following set:{3,5,6,8,13}

Answer 1

To find the variance and standard deviation, we need to find the mean first.

`\begin{gathered} \mu=(\sum x_i)/(n) \\ \text{where} \\ x_i\text{ is the data set} \\ n\text{ is the number of data} \end{gathered}`
`\begin{gathered} \mu=(3+5+6+8+13)/(5) \\ \mu=(35)/(5) \\ \mu=7 \end{gathered}`

Now that we have the mean, we can now solve for variance.

`\begin{gathered} \text{Variance is written as }\sigma^2 \\ \sigma^2=(\sum (x_i-\mu)^2)/(n) \\ \\ \sigma^2=((3-7)^2+(5-7)^2+(6-7)^2+(8-7)^2+(13-7)^2)/(5) \\ \sigma^2=((-4)^2+(-2)^2+(-1)^2+(1)^2+(6)^2)/(5) \\ \sigma^2=(16+4+1+1+36)/(5) \\ \sigma^2=(58)/(5) \\ \sigma^2=11.6 \end{gathered}`

The variance is equal to 11.6.

To find the standard deviation, get the square root of the variance.