The following table presents the heights (in inches) of a sample of college basketball play
$\begin{array}{cc}
\hline \text { Height (in.) } & \text { Frequency } \
\hline 68-71 & 11 \
72-75 & 56 \
76-79 & 54 \
80-83 & 40 \
84-87 & 13 \
\hline
\end{array}$
Considering the data to be a population, approximate the standard deviation of the heights .
A) 77.7
B) 4.2
C) 17.6
D) 4

Question

Quizplus · Accepted Answer

To approximate the standard deviation of the heights, we first need to calculate the mean height. We do this by finding the midpoint of each height interval, multiplying each midpoint by the corresponding frequency, summing these products, and then dividing by the total number of observations. After calculating the mean, we use the formula for standard deviation, which involves subtracting the mean from each midpoint, squaring these differences, multiplying by the corresponding frequencies, summing these products, dividing by the total number of observations, and finally taking the square root of this result. The correct answer is approximately 4.2 inches, indicating the average amount by which individual heights deviate from the mean height in the population.

The Following Table Presents the Heights (In Inches) of a Sample