Statistics

A histogram is a graph that displays the classes on the horizontal axis and the frequencies of the classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is equal to the frequency of the class (when all the class widths are equal).

The exam scores of a group of students are given by the following table:

Score	0-19	20-39	40-59	60-79	80-99
Frequency	5	4	6	2	1

Construct the histogram.

A histogram is similar to a bar graph. However bar charts are not appropiate for data with grouped frequencies for ranges of values, instead we use a histogram which is a diagram in which rectangles are used to represent frequencies. A histogram differs from the bar chart in that the rectangles may have different widths, but the key feature is that, for each rectangle area is proportional to class frequency.

Histograms with unequal class widths
To construct a histogram with nequal class widths we must make the area of each bar represent the frequency of items in the group. We do this by making:

The width of a bar the same as the class width of the group it represents.
The height of a bar equal to (this fraction is called the frequency density)

The following table shows the distribution of the ages of people boarding buses at the bus station between 08:30 and 09:00 one morning:

Age, n years
Frequency	10	20	30	20	15

Draw a histogram.