Histograms

• Histograms show grouped continuous data, with no gaps between the bars.
• Frequency density = frequency ÷ class width. Label the vertical axis “Frequency density”.
• The area of each bar represents its frequency: frequency = frequency density × class width.
• With unequal class widths, compare frequency densities, not heights of a frequency axis.
• Estimate the number of values in part of a class by assuming they are spread evenly through it.

Bar height = frequency ÷ width

When the classes have different widths, a wide class would look too important if its bar height were its frequency. Dividing by the class width fixes this. Draw each bar from its lower to its upper class boundary, on a continuous scale, with height equal to the frequency density.

Area of the bar

To get a frequency back from a histogram, multiply the bar’s height (frequency density) by its width. Adding all the bars gives the total.

Find the scale from a known bar

Sometimes the frequency density axis has no scale, but one class’s frequency is given. Use that bar to find how much frequency density one unit of height represents, then apply it to every other bar.