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All 6 members of a family work. Their hourly wages (in dollars) are the following26, 7, 23, 15, 29, 24Send data to calculatorAssuming that these wages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)0

Answer :

Then To determine the standard deviation we first need the mean; the mean is given by:

[tex]\mu=\frac{1}{n}\sum_{i\mathop{=}1}^nx_i[/tex]

Then we have:

[tex]\mu=\frac{1}{6}(26+7+23+15+29+24)=\frac{124}{6}=20.67[/tex]

Now that we have the mean we can calculate the standard deviation which is given by:

[tex]\sigma=\sqrt{\frac{1}{n}\sum_{i\mathop{=}1}^n(x_i-\mu)^2}[/tex]

Then we have:

[tex]\begin{gathered} \sigma=\sqrt{\frac{(26-20.67)^2+(7-20.67)^2+(23-20.67)^2+(15-20.67)^2+(29-20.67)^2+(24-20.67)^2}{6}} \\ \sigma=7.45 \end{gathered}[/tex]

Therefore, the standard deviation is 7.45

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