Sheet № 120 · Higher only · AQA · Edexcel · OCR
Drawing & Reading Histograms –
Histograms are a Higher-tier topic that consistently appears on AQA, Edexcel and OCR papers. The key difference between a histogram and a bar chart is that a histogram uses frequency density on the vertical axis, and the area of each bar — not its height — represents the frequency. This guide focuses on the practical skills of drawing his
§Key definitions
Question:
The table shows the ages of 80 members of a gym. Draw a histogram.
Answer:
The histogram has four bars with frequency densities 2.0, 2.4, 1.6, and 1.0 respectively.
Q1 (Foundation):
Calculate the frequency densities for these reaction times.
Q2 (Foundation):
A histogram bar covers the interval 50 ≤ x < 80 and has a frequency density of 1.5. Find the frequency.
Q3 (Higher):
A histogram bar covers 20 ≤ w < 35 with a frequency density of 4. Estimate how many data values fall between 20 and 25.
§Formulas to memorise
Frequency density = Frequency ÷ Class width
Frequency = Frequency density × Class width
Calculate the class width — for each interval (upper boundary minus lower boundary).
Calculate the frequency density — for each class: frequency ÷ class width.
Draw — the horizontal axis with a continuous scale showing class boundaries (no category labels).
Draw — each bar from the lower to the upper boundary with height equal to the frequency density.
Label — the vertical axis "Frequency density" — never "Frequency".
Worked example
The table shows the ages of 80 members of a gym. Draw a histogram. | Age (years) | 15-24 | 25-34 | 35-44 | 45-64 | |---|---|---|---|---| | Frequency | 20 | 24 | 16 | 20 |
Working: Class widths: 10, 10, 10, 20. Frequency densities: 20÷10=2.0, 24÷10=2.4, 16÷10=1.6, 20÷20=1.0. Draw the horizontal axis from 15 to 65. Draw bars at heights 2.0, 2.4, 1.6, and 1.0 with no gaps.
⚠ Common mistakes
- ✗Plotting frequency instead of frequency density. If class widths are unequal, this distorts the diagram. Always calculate frequency density first.
- ✗Leaving gaps between bars. Histograms represent continuous data, so bars must touch with no gaps.
- ✗Misreading the axis when recovering frequency. To find frequency from a histogram, multiply the height (frequency density) by the class width — do not just read the height as the frequency.
✦ Exam tips
- →Always show the frequency density calculations in a table alongside your diagram. Examiners award marks for this working.
- →Use a ruler and sharp pencil for accurate bars. Check that the boundaries align exactly with the scale.
- →When estimating a frequency within part of a class, assume the data is evenly distributed and use the proportion of the class width.