Find the standard deviation for the scores: $$\begin{array} { l l l l l }
21 & 32 & 28 & 25 & 23 \
30 & 26 & 28 & 27 & 28
\end{array}$$
A)26.8
B)3.06
C)3.22
D)10.4

Question

Find the standard deviation for the scores: $$\begin{array} { l l l l l } 
21 & 32 & 28 & 25 & 23 \
30 & 26 & 28 & 27 & 28
\end{array}$$
A)26.8
B)3.06
C)3.22
D)10.4

Quizplus · Accepted Answer

1. Find the mean: 
\begin{align*}
\text{Mean }&= \frac{21 + 32 + 28 + 25 + 23 + 30 + 26 + 28 + 27 + 28}{10} \
&= \frac{268}{10} \
&= 26.8
\end{align*}
2. Calculate the deviations from the mean: 
$$\begin{array} { l l l l l } 
-5.8 & 5.2 & 1.2 & -1.8 & -3.8 \
3.2 & -0.8 & 1.2 & 0.2 & 1.2
\end{array}$$
3. Square the deviations: 
$$\begin{array} { l l l l l } 
33.64 & 27.04 & 1.44 & 3.24 & 14.44 \
10.24 & 0.64 & 1.44 & 0.04 & 1.44
\end{array}$$
4. Sum the squared deviations: 94.36
5. Divide the sum by the number of scores (10): 
$$\frac{94.36}{10} = 9.436$$
6. Take the square root of the result: 
$$\sqrt{9.436} \approx \boxed{3.22}.$$

Find the Standard Deviation for the Scores 21322825233026282728\begin{array} { l l l l l } 21 & 32 & 28 & 25 & 23 \\30 & 26 & 28 & 27 & 28\end{array}2130​3226​2828​2527​2328​

Find the Standard Deviation for the Scores $\begin{array} { l l l l l } 21 & 32 & 28 & 25 & 23 \\30 & 26 & 28 & 27 & 28\end{array}$