Answer: 12.02
Explanation:
Calculating the standard deviation of the large wild cats.
The data set is:
[tex]70,50,35,50,40,40,35,45,25[/tex]The numbers represent speed in miles per hour.
Step 1. The first step is to remember the formula to calculate standard deviation:
[tex]\sigma=\sqrt[]{\frac{\sum^{}_{}(x-\operatorname{mean})^2}{n}}[/tex]Where
σ --> standard deviation
x --> values from the data set
mean --> mean of the data set
n --> number of values in the data set
∑ --> sum of (x-mean)^2 values for each x value.
Step 2. In our case:
[tex]n=9[/tex]Let's calculate the mean of the data set by adding all of the values and dividing the result by 9:
[tex]\begin{gathered} \operatorname{mean}=\frac{70+50+35+50+40+40+35+45+25}{9} \\ \downarrow\downarrow \\ \operatorname{mean}=\frac{390}{9} \end{gathered}[/tex]The result is:
[tex]\operatorname{mean}=43.333[/tex]Step 3. Substitute all of the values into the standard deviation formula:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{\sum^{}_{}(x-\operatorname{mean})^2}{n}} \\ \downarrow\downarrow \\ \sigma=\sqrt[]{\frac{(70-43.333)^2+(50-43.333)^2+(35-43.333)^2+(50-43.333)^2+(40-43.333)^{2+}(40-43.333)^2+(35-43.333)^2+(45-43.333)^2+(25-43.333)^2}{9}} \\ \end{gathered}[/tex]The result is:
[tex]\sigma=\sqrt[]{\frac{1300}{9}}[/tex]Solving the operations:
[tex]\begin{gathered} \sigma=\sqrt[]{144.44} \\ \sigma=12.02 \end{gathered}[/tex]Answer: 12.02
