Question

Listed below are the heights of 5 small cacti, in inches: {8 13 15 17 22} Find the variance and the standard of deviation of the data.

Answer 1

you will have to use the variance formula

`s^2=\frac{\sum ^(\infty)_(n\mathop=0)(x_i-\bar{x})^2}{n-1}`

where n is the number of data that was given

start by calculating the average

`\begin{gathered} \bar{x}=(8+13+15+17+22)/(5) \\ \bar{x}=15 \end{gathered}`

replace on the formula

`\begin{gathered} s^2=((8-15)^2+(13-15)^2+(15-15)^2+(17-15)^2+(22-15)^2)/(4) \\ s^2=(106)/(4) \\ s^2=26.5 \end{gathered}`

the variance will be 26.5

to calculate the standard deviation you do the square root of the variance

`\begin{gathered} s=\sqrt[]{26.5} \\ s\approx5.148 \end{gathered}`