Histograms and Frequency Density

Statistics - investigating histograms with variable interval widths, and frequency densities

KS4, GCSE Higher Mathematics, Statistics - KS5 AS Level Statistics (S1)

Instructions below    Waldomaths video    Waldomaths video    Waldomaths video    See also: Cumulative Frequency

[Applet - graphs of hyperbolic functions ]

As you start this applet, you'll see a frequency distribution drawn on the screen. The intervals are all the same width (10). But what happens if the widths of the intervals are not the same?
Well, you can see by varying them yourself. Click and drag the little circles at the interval boundaries, and the distribution is redrawn with new intervals. Notice how this distorts the shape of the distribution.
Now click the "Histogram +/-" button. The distribution is redrawn, but this time the vertical axis is the frequency density, which is the frequency divided by the width of the interval.

Notice what happens when you vary the interval widths now. The general shape of the distribution stays much more like the original screen. Try it and see. Pressing "Reset" shows the original.
The main point of this applet is to demonstrate why we use frequency densities rather than frequencies for drawing distributions with variable interval widths. The answer is simple - there is much less distortion, and so the shape of the distribution tells us much more about the underlying data.