Charts, tables and when to use them

Tier: #Foundation #Higher

How to

The type of data you have determines which chart or table to use. Picking the wrong one is a common mistake in data questions.

Bar charts — comparing frequencies across categories (e.g. favourite subjects). Bars should be equal width with gaps between them.

Pie charts — showing proportions of a whole. Calculate each angle using: $$\text{angle} = \frac{\text{frequency}}{\text{total}} \times 360°$$

Frequency tables — the starting point for almost all data questions. Use grouped frequency tables (with class intervals) when the data range is large.

Two-way tables — show two categories at once. Rows and columns should each add up to their totals — use this to fill in any missing values.

Scatter graphs — plot two numerical variables to look for a relationship. See Correlation for how to interpret them.

Histograms — for grouped continuous data where the class widths may vary. The y-axis shows frequency density, not frequency: $$\text{frequency density} = \frac{\text{frequency}}{\text{class width}}$$

Cumulative frequency graphs — show a running total of frequencies. Used to find the median, quartiles, and interquartile range.

The golden rule: match the chart to the data type. Categorical → bar chart or pie chart. Continuous → histogram. Two variables → scatter graph. Running totals → cumulative frequency.

Questions to practise
📝Past paper questions
💬What the examiners say
  • "Students needed to state their observations clearly and unambiguously, identifying the specific axis or feature at issue. Labelling of the diagram proved to be a help to students and is to be encouraged."
  • "Points should be plotted at the upper class boundary."
  • "It is recommended that points are joined with straight lines using a ruler rather than freehand."
⬆️How you can quickly improve
  • Always plot cumulative frequency points at the upper boundary of each class interval, not the midpoint.
  • Before reading from a graph, calculate the position you need — total ÷ 2 for the median, total ÷ 4 for the lower quartile — and write it down before drawing any lines.
  • Structure every statistical comparison as a complete sentence: give a value for each group, then compare directly using words like 'higher', 'lower', or 'greater'.
💡Watch
🔓What this unlocks
ℹ️Calculator tricks