Histograms

Last time

Before we start: last time, in Cumulative frequency and box-and-whisker plots, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

When the groups are not equal

A bar chart works when every group is the same width. But times might be grouped as zero to ten, ten to fifteen, fifteen to twenty-five. A tall wide bar would look far bigger than it really is. A histogram fixes this with one change: the height is the frequency density, and the area of each bar is the frequency.

Frequency density

Frequency density is the frequency divided by the class width. It tells you how crowded each bit of the scale is. A class from ten to fifteen has a width of five. If thirty people are in it, the frequency density is six. The area of a bar, width times height, then gives back the frequency.

Drawing a histogram

Classes: zero to ten, frequency twenty, width ten, so density two. Ten to fifteen: thirty, width five, density six. Fifteen to twenty-five: forty, width ten, density four. Twenty-five to forty-five: twenty, width twenty, density one. Draw bars with no gaps. The width of each bar is the class width, the height is the density.