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=\frac{\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=\frac{3+5+6+8+13}{5} \\ \mu=\frac{35}{5} \\ \mu=7 \end{gathered}$

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

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

The variance is equal to 11.6.

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

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