Unequal class widths and two-variable data
Draw a histogram with classes of different widths using frequency density, read the frequency back from a bar, and read two variables of the same people on one graph.
- UK: Year 10
- Iran: grade 10
- Afghanistan: grade 11
Guide
When the classes of a histogram have different widths, the height cannot be the frequency, because a wide class would look bigger just for being wide. Use frequency density: frequency ÷ class width. Then the area of a bar (width × height) is the frequency.
To draw it: work out the frequency density of each class, draw the bars from class boundary to class boundary, and label the vertical axis "frequency density". To read it back: frequency = class width × frequency density.
Data with two variables, such as height and weight of the same people, are drawn on one scatter graph: each person is one point. A line at a value of each variable cuts the graph into four regions, and we can count the people in a region, for example the tall and heavy ones.