Question

find the standard deviation of the data set:{5, 8, 11, 13, 17, 18}(do not round until the final answer. Then round two decimal places as needed.)

Answer 1

The standard deviation of a data is given by:

`\sigma=\sqrt[]{\frac{\sum ^{}_{}(x-\mu)^2}{n-1}}`

the summation is over all the elements of the data and μ is the mean of the data, n is the number of elements.

Calculate the mean μ as follow:

`\mu=\frac{\sum ^{}_{}x}{n}=(5+8+11+13+17+18)/(6)=12`

Next, replace the values of the parameters into the formula for the standard deviation and simplify:

`\begin{gathered} \sigma=\sqrt[]{((5-12)^2+(8-12)^2+(11-12)^2+(13-12)^2+(17-12)^2+(18-12)^2)/(6-1)} \\ \sigma\approx5.06 \end{gathered}`

Hence, the standard deviation of the given data is approximately 5.06