Question

the heights (in inches) for a sample of 14 male adults are 62, 82, 79, 76, 73, 70, 79, 79, 75, 75, 75, 72, 72, 72. draw the histogram for these data using an initial class boundary of 61.5 and a class width of 6. note that you can add or remove classes from the figure. label each class with its endpoints.

Explanation:

Step1: Determine class boundaries

Given initial class boundary \(61.5\) and class width \(6\).
First class: \(61.5 - 67.5\)
Second class: \(67.5 - 73.5\)
Third class: \(73.5 - 79.5\)
Fourth class: \(79.5 - 85.5\)

Step2: Count frequencies

• For \(61.5 - 67.5\): \(1\) (only \(62\))
• For \(67.5 - 73.5\): \(5\) (\(70,72,72,72,73\))
• For \(73.5 - 79.5\): \(6\) (\(75,75,75,76,79,79,79\))
• For \(79.5 - 85.5\): \(1\) (only \(82\))

Answer:

Class Boundaries	Frequency
\(67.5 - 73.5\)	\(5\)
\(73.5 - 79.5\)	\(6\)
\(79.5 - 85.5\)	\(1\)

Now, to draw the histogram:

• The \(x -\)axis (horizontal axis) is labeled "Height (in inches)" with class boundaries \(61.5 - 67.5\), \(67.5 - 73.5\), \(73.5 - 79.5\), \(79.5 - 85.5\)
• The \(y -\)axis (vertical axis) is labeled "Frequency" with values from \(0\) to \(8\) (since the maximum frequency is \(6\)).
• Draw bars with heights corresponding to the frequencies: height \(1\) for \(61.5 - 67.5\), height \(5\) for \(67.5 - 73.5\), height \(6\) for \(73.5 - 79.5\), and height \(1\) for \(79.5 - 85.5\)