Respuesta :
The rule of the standard deviation of data is
[tex]\sigma=\sqrt{\frac{\sum_^(x-\mu)^2}{n}}[/tex]Where n is the number of data
μ is the mean
To find the mean sum of the data given and divide it by n
Since the given data are
[tex]223,225,300,291,289,267,171,166,141[/tex]Then n = 9
[tex]\begin{gathered} \mu=\frac{223+225+300+291+289+267+171+166+141}{9} \\ \\ \mu=\frac{691}{3} \end{gathered}[/tex]Now, we will subtract the mean from each data, then ann the answers
[tex]223-\frac{691}{3}=(-\frac{22}{3})^2=\frac{484}{9}[/tex][tex]225-\frac{691}{3}=(-\frac{16}{3})^2=\frac{356}{9}[/tex][tex]300-\frac{691}{3}=(\frac{209}{3})^2=\frac{43681}{9}[/tex][tex]291-\frac{691}{3}=(\frac{182}{3})^2=\frac{33124}{9}[/tex][tex]289-\frac{691}{3}=(\frac{176}{3})^2=\frac{30976}{9}[/tex][tex]267-\frac{691}{3}=(\frac{110}{3})^2=\frac{12100}{9}[/tex][tex]171-\frac{691}{3}=(-\frac{178}{3})^2=\frac{31684}{9}[/tex][tex]166-\frac{691}{3}=(-\frac{193}{3})^2=\frac{37249}{9}[/tex][tex]141-\frac{691}{3}=(-\frac{268}{3})^2=\frac{71824}{9}[/tex]We will add all of these answers and divide them by n
[tex]\begin{gathered} \sigma=\sqrt{\frac{\frac{261478}{9}}{9}} \\ \\ \sigma=56.8 \end{gathered}[/tex]The answer is D
