Frequency density
- A histogram shows grouped continuous data, often with unequal class widths. The bars touch, and the area of each bar shows the frequency.
- Frequency density = frequency ÷ class width. It goes on the vertical axis.
- A group 10 < t ≤ 30 with a frequency of 16 has a class width of 20 and a frequency density of 16 ÷ 20 = 0.8.
Reading a histogram
- Frequency = frequency density × class width.
- To estimate how many values are in part of a group, use that part of the bar: half the width holds about half the frequency.
Drawing a histogram
- Work out the class width and frequency density for each group. Draw bars with no gaps, from the start to the end of each group.
- Label the vertical axis 'frequency density', not 'frequency'.
Why use a histogram?
- If the groups have different widths, a bar chart of frequencies is misleading, because wide groups look too big. Using area keeps the comparison fair.
Key terms
- Histogram
- A chart for grouped continuous data where the area of each bar shows the frequency.
- Frequency density
- Frequency ÷ class width.
- Class width
- The size of a group, such as 20 for 10 < t ≤ 30.
- Continuous data
- Data that can take any value in a range, such as time or height.
- Area
- For a histogram bar, frequency density × class width = frequency.