Using the data table shown, what is the standard deviation of the number of species' bones found in 40 sets of stomach contents collected from coyotes?
?
Number of species' bones found in 40 sets of stomach contents from coyotes.

$\begin{array}{l}
\text { Number }\
\begin{array}{cc}
\text { of bones } & \text { Frequency } \
\hline 0 & 3 \
1 & 7 \
2 & 10 \
3 & 5 \
4 & 12 \
5 & 6
\end{array}
\end{array}$ ?

Question

Using the data table shown, what is the standard deviation of the number of species' bones found in 40 sets of stomach contents collected from coyotes?
?
Number of species' bones found in 40 sets of stomach contents from coyotes.

$\begin{array}{l}
\text { Number }\
\begin{array}{cc}
\text { of bones } & \text { Frequency } \
\hline 0 & 3 \
1 & 7 \
2 & 10 \
3 & 5 \
4 & 12 \
5 & 6
\end{array}
\end{array}$ ?

Quizplus · Accepted Answer

To calculate the standard deviation, we first need to find the mean (average) number of bones. We do this by multiplying each number of bones by its frequency, summing those products, and then dividing by the total number of sets of stomach contents (40).Mean calculation:$$ \text{Mean} = \frac{(0*3) + (1*7) + (2*10) + (3*5) + (4*12) + (5*6)}{40} = \frac{0 + 7 + 20 + 15 + 48 + 30}{40} = \frac{120}{40} = 3 $$Next, we calculate the variance by taking each number of bones, subtracting the mean, squaring the result, multiplying by the frequency, summing these products, and then dividing by the total number of sets of stomach contents.Variance calculation:$$ \text{Variance} = \frac{(0-3)^2*3 + (1-3)^2*7 + (2-3)^2*10 + (3-3)^2*5 + (4-3)^2*12 + (5-3)^2*6}{40} $$$$ = \frac{9*3 + 4*7 + 1*10 + 0*5 + 1*12 + 4*6}{40} $$$$ = \frac{27 + 28 + 10 + 0 + 12 + 24}{40} $$$$ = \frac{101}{40} = 2.525 $$Finally, the standard deviation is the square root of the variance:$$ \text{Standard deviation} = \sqrt{2.525} \approx 1.59 $$However, none of the provided choices exactly match this calculation. Given the choices, it seems there might have been a misunderstanding or miscalculation. Based on the standard approach to calculating standard deviation, none of the provided choices (A) 1.8, (B) 2.0, (C) 2.2, (D) 2.4 directly match the calculated result. A reevaluation of the calculation steps or the choices might be necessary.

Using the Data Table Shown, What Is the Standard Deviation