A histogram is a graphical summary of a frequency distribution of a data set, that is, it is a summary of classes (groups) of data values and the frequencies for those classes.
When constructing a histogram for a data set,
it is necessary to break up the range of data values into classes and to count the number of
observations that fall into each class.
The histogram for the data set in this problem is required to have an initial class boundary of  , an ending class boundary
of  , and  classes. The
initial
class boundary is the left endpoint of the first class, and the
ending class boundary is the right endpoint of the last class.
In order to determine the classes, we need
to break up the interval ranging from up to into intervals of equal width. (For convenience, classes are almost always of equal width.)
Since  , the width of each class is . Thus,
the classes are
| Height (in inches) |
Frequency |
| 60.5 up to 65.5 |
4 |
| 65.5 up to 70.5 |
4 |
| 70.5 up to 75.5 |
9 |
| 75.5 up to 80.5 |
4 |
| 80.5 up to 85.5 |
1 |
|
| Table 1 |
up to  , | up to  , | up to  , | up to  , | | up to . |
Now we need to calculate the frequency for each class, that is, we need to find the number of measurements that fall within
each class. The frequencies are easily found after sorting the
data. The sorted data are
61, 62, 63, 64, 66, 67, 69, 70, 72, 72, 72, 72, 73, 75, 75, 75, 75, 76, 79, 79, 80, 82.
Table 1 displays the frequencies, which you should verify from the sorted data.
| Quick Note | What is the difference between a histogram and a frequency polygon?
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In a histogram, classes are displayed on the horizontal axis, and class frequencies are displayed on the vertical axis. The histogram consists of rectangles whose widths indicate the classes and whose heights indicate the class frequencies.
Classes are labeled by their left and right endpoints (though sometimes the midpoints are used instead).
Using Table 1, we draw the histogram for the data set given in the problem.
The answer is:
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