To construct a histogram, divide continuous data into equal class intervals, place those intervals on the horizontal axis, and draw touching bars whose heights show the frequency in each interval. In IB Mathematics: Analysis and Approaches SL 4.2, frequency-density histograms are not required, so examination questions use equal-width intervals.
Construction Method
- Organize the data. Create a frequency table showing how many observations fall within each interval. Use inequalities to make the boundaries unambiguous.
| Class interval | Frequency |
|---|---|
| 3 | |
| 7 | |
| 5 | |
| 2 |
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Draw and label the axes. Put the measured variable and its units on the horizontal axis. Label the vertical axis frequency.
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Choose suitable scales. The horizontal scale must preserve the numerical spacing of the class boundaries. The vertical scale should begin at zero and extend beyond the greatest frequency.
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Draw the bars. For the example, draw bars of heights , , , and . Each bar extends across its complete class interval, and adjacent bars touch because the data are treated as continuous.
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Check the graph. Confirm that every interval has one bar, the bar heights match the frequencies, and both axes are clearly labelled.
Common Misconception
A histogram is not a bar chart. Histogram bars touch and represent numerical intervals; bar-chart bars are separated because they represent distinct categories. Also, do not calculate frequency density for IB Math AA SL 4.2: frequency-density histograms are explicitly outside the required syllabus.
Exam Technique
This is AA SL content studied by both SL and HL students and may appear on Paper 1 or Paper 2. For a command such as construct, examiners expect an accurate graph with labelled axes, a consistent scale, correct class boundaries, touching bars, and correct heights.
