25.3 Histograms — Learn

Prerequisites: calculate class widths, divide, and read grouped frequency tables.

Objectives: calculate frequency density and use it to draw and interpret a histogram.

A histogram represents grouped continuous data. Its bars touch. The area of each bar represents frequency.

Example 1. A class from 0 to 10 has frequency 20. Find its frequency density.

The class width is $10-0=10$.

Frequency density $=20/10=2$.

The bar has width 10 and height 2, so its area is $10\times2=20$.

Example 2. A second class from 10 to 30 has frequency 30.

The class width is $30-10=20$.

Frequency density $=30/20=1.5$.

Draw the first bar from 0 to 10 with height 2. Draw the second from 10 to 30 with height 1.5. Label the horizontal axis with the measured variable and the vertical axis with frequency density.

Watch out. Bar height is not always frequency. For unequal widths, use frequency density; check each bar's area by multiplying width by height.

Progress check

The chapter travel-time classes have unequal widths in many surveys. Why would bar heights equal to frequency misrepresent such data?

You should now be able to

• find a class width from its boundaries;
• calculate frequency density;
• draw and interpret a histogram with unequal class widths.