Answer: 12.02
Step-by-step explanation:
Calculating the standard deviation of the large wild cats.
The data set is:
The numbers represent speed in miles per hour.
Step 1. The first step is to remember the formula to calculate standard deviation:
![\sigma=\sqrt[]{\frac{\sum^{}_{}(x-\operatorname{mean})^2}{n}}]()
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:
Let's calculate the mean of the data set by adding all of the values and dividing the result by 9:
![\begin{gathered} \operatorname{mean}=(70+50+35+50+40+40+35+45+25)/(9) \\ \downarrow\downarrow \\ \operatorname{mean}=(390)/(9) \end{gathered}]()
The result is:
![\operatorname{mean}=43.333]()
Step 3. Substitute all of the values into the standard deviation formula:
![\begin{gathered} \sigma=\sqrt[]{\frac{\sum^{}_{}(x-\operatorname{mean})^2}{n}} \\ \downarrow\downarrow \\ \sigma=\sqrt[]{((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}]()
The result is:
![\sigma=\sqrt[]{(1300)/(9)}](https://img.qammunity.org/2023/formulas/mathematics/college/mme21u785dalth1ir71f3u7tc47txaka0d.png)
Solving the operations:
![\begin{gathered} \sigma=\sqrt[]{144.44} \\ \sigma=12.02 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/9dzrwrj62hw60ijy8yng30c5wxcovjerd7.png)
Answer: 12.02