From the following grouped data, find the sample standard deviation. $$\begin{array} { | l | l | l | l | }
\hline \text { Interval } & \text { Midpoint } x & \text { Frequency } f & \text { Product } x f \
\hline 41.5 - 48.5 & & 10 & \
\hline 48.5 - 55.5 & & 16 & \
\hline 55.5 - 62.5 & & 18 & \
\hline 62.5 - 69.5 & & 25 & \
\hline 69.5 - 76.5 & & 4 & \
\hline 76.5 - 83.5 & & 1 & \
\hline
\end{array}$$ Round your answer to the nearest whole number.
A) 5
B) 17
C) 8
D) 11
E) 7

Question

From the following grouped data, find the sample standard deviation. $$\begin{array} { | l | l | l | l | } 
\hline \text { Interval } & \text { Midpoint } x & \text { Frequency } f & \text { Product } x f \
\hline 41.5 - 48.5 & & 10 & \
\hline 48.5 - 55.5 & & 16 & \
\hline 55.5 - 62.5 & & 18 & \
\hline 62.5 - 69.5 & & 25 & \
\hline 69.5 - 76.5 & & 4 & \
\hline 76.5 - 83.5 & & 1 & \
\hline
\end{array}$$ Round your answer to the nearest whole number.
A) 5
B) 17
C) 8
D) 11
E) 7

Quizplus · Accepted Answer

1. Find the mean: 
\begin{align*}
\bar{x} &= \frac{\sum{x f}}{\sum{f}}\
&= \frac{(46 	imes 10)+(52 	imes 16)+(59 	imes 18)+(66 	imes 25)+(73 	imes 4)+(80 	imes 1)}{74}\
&= 60.
\end{align*}

2. Find the variance: 
\begin{align*}
s^2 &= \frac{\sum{f x^2}-n\bar{x}^2}{n-1}\
&= \frac{(10 	imes 46^2)+(16 	imes 52^2)+(18 	imes 59^2)+(25 	imes 66^2)+(4 	imes 73^2)+(1 	imes 80^2)-74(60)^2}{73}\
&\approx 69.55
\end{align*}

3. Find the standard deviation: 
\begin{align*}
s &= \sqrt{s^2}\
&\approx \sqrt{69.55}\
&\approx 8.
\end{align*}

Therefore, the answer is C.

From the Following Grouped Data, Find the Sample Standard Deviation