Frequency distribution of the scores from a mathematics test is given in the table below. Find the sample standard deviation. $$\begin{array} { | l | l | l | l | }
\hline \text { Interval } & \text { Midpoint } x & \text { Frequency } f & \text { Product } x f \
\hline 64.5 - 70.5 & & 4 & \
\hline 70.5 - 76.5 & & 7 & \
\hline 76.5 - 82.5 & & 7 & \
\hline 82.5 - 88.5 & & 5 & \
\hline 88.5 - 94.5 & & 2 & \
\hline 94.5 - 100.5 & & 6 & \
\hline
\end{array}$$ Round your answer to the nearest whole number.
A) 12
B) 10
C) 18
D) 17
E) 8

Question

Frequency distribution of the scores from a mathematics test is given in the table below. Find the sample standard deviation.   $$\begin{array} { | l | l | l | l | } 
\hline \text { Interval } & \text { Midpoint } x & \text { Frequency } f & \text { Product } x f \
\hline 64.5 - 70.5 & & 4 & \
\hline 70.5 - 76.5 & & 7 & \
\hline 76.5 - 82.5 & & 7 & \
\hline 82.5 - 88.5 & & 5 & \
\hline 88.5 - 94.5 & & 2 & \
\hline 94.5 - 100.5 & & 6 & \
\hline
\end{array}$$ Round your answer to the nearest whole number.
A) 12
B) 10
C) 18
D) 17
E) 8

Quizplus · Accepted Answer

To find the sample standard deviation, first calculate the midpoints for each interval, then find the mean using the midpoints and frequencies. Next, calculate the variance by finding the squared differences from the mean, weighted by frequency, and divide by the total frequency minus one. Finally, take the square root of the variance to get the standard deviation. The calculations yield a standard deviation of approximately 10.

Frequency Distribution of the Scores from a Mathematics Test Is