Data Presentation and Display
What you must understand
Choosing an appropriate display depends on the type of data. For qualitative data use bar charts (gaps between bars) and pie charts (proportions of a whole). For quantitative data use histograms (continuous, bars touching, frequency on the vertical axis and class boundaries on the horizontal), frequency polygons, cumulative frequency curves (ogives), stem-and-leaf diagrams, scatter diagrams and box-and-whisker plots. You should be able to read and construct tally and frequency tables, including grouped frequency tables with correct class boundaries.
Know the vocabulary: class limits (as written), class boundaries (the true dividing points, e.g. 10–19 has boundaries 9.5–19.5), class width, class midpoint, and frequency density (= frequency ÷ class width) when classes are unequal.
Traps that appear in questions
- Drawing a histogram with frequency on the vertical axis when class widths differ; with unequal widths you must plot frequency density.
- Leaving gaps between histogram bars, or inserting gaps between bar-chart bars.
- Plotting an ogive against upper class limits rather than upper class boundaries.
- Misreading a pie chart: each sector's angle = (frequency ÷ total) × 360°.
- Forgetting that a stem-and-leaf diagram needs a key (e.g. 4 | 2 means 42).
Worked example
Frequencies: 0–9: 8; 10–19: 12; 20–39: 20. Draw the histogram heights.
Answer: Widths are 10, 10 and 20. Frequency densities are 8/10 = 0.8, 12/10 = 1.2 and 20/20 = 1.0. Plot these heights on the vertical axis against boundaries 0, 9.5, 19.5, 39.5 (remember the first class boundary is −0.5 if the data are whole numbers starting at 0).
Rule of thumb: bars touch for continuous data (histogram), bars are separated for categories (bar chart).