Topic 2 of 7 · Form 3
Presentation of data
Frequency tables, grouped frequency tables, class boundaries, class widths and two-way tables.
Notes for this topic 1 file, in order
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Tables
Frequency tables, grouped frequency tables, class boundaries, class widths and two-way tables.
Diagrams
Bar charts (simple, compound, component), pie charts (angle = frequency ÷ total × 360°), pictograms, stem-and-leaf diagrams, histograms (frequency density = frequency ÷ class width for unequal widths), frequency polygons, cumulative frequency curves (plotted at upper class boundaries) and box-and-whisker plots.
Worked example: Classes 0–10 (frequency 15), 10–30 (frequency 40), 30–60 (frequency 30). Find the frequency densities.
1.5, 2.0 and 1.0
Choosing a diagram
Pie charts for proportions; bar charts for comparisons; histograms for continuous grouped data; cumulative frequency for medians and quartiles.
Misleading diagrams
Broken axes, unequal scales, 3D effects and pictograms with distorted areas.
Check yourself
- A pie chart represents 240 people. What angle represents 50 people?
- Where are points plotted on a cumulative frequency curve?
- Why can a histogram with unequal class widths not use frequency on the vertical axis?
Show answers
- 50 ÷ 240 × 360 = 75°
- At the upper class boundaries.
- The area, not the height, must represent frequency, so frequency density is needed.
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