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How do you construct and interpret bar charts, pictograms, pie charts, frequency diagrams and histograms?

Construct and interpret bar charts, pictograms, vertical line graphs, pie charts and frequency diagrams, and at Higher tier draw and interpret histograms using frequency density for unequal class widths.

A focused answer to the WJEC GCSE Mathematics statistics content on charts and graphs, covering bar charts, pictograms, vertical line graphs, pie charts and frequency diagrams, and histograms with frequency density for unequal class widths at Higher tier.

Generated by Claude Opus 4.812 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. Bar charts, pictograms and line graphs
  3. Pie charts
  4. Histograms (Higher)
  5. Reading a histogram
  6. Why this matters

What this dot point is asking

WJEC asks you to construct and interpret the main statistical diagrams: bar charts, pictograms, vertical line graphs, pie charts and frequency diagrams, and at Higher tier to draw and read histograms with unequal class widths using frequency density. The skill is matching the diagram to the data type and reading values off accurately, and the Higher histogram is the topic's discriminator because it uses area, not height, to represent frequency. These appear across both components, often combined with averages or with interpreting a real data set.

Bar charts, pictograms and line graphs

These suit discrete or categorical data.

A bar chart has bars of equal width, separated by gaps, with height showing frequency, suitable for categories or discrete values. A pictogram uses a repeated symbol with a key stating how many each symbol represents, so half a symbol is half that value. A vertical line graph plots discrete data as thin lines. All are read by matching the bar or symbol to the frequency scale, and constructing them requires a sensible, evenly spaced scale.

Pie charts

A pie chart shows how a whole divides into proportions.

So if 9090 people are surveyed, each person is worth 360∘÷90=4∘360^\circ \div 90 = 4^\circ, and a category chosen by 2020 people takes 80∘80^\circ. The angles must sum to 360∘360^\circ, a useful check.

Histograms (Higher)

A histogram looks like a bar chart but represents grouped continuous data, and the bars can have different widths.

This is the single most error-prone idea in the topic: plotting frequency as the height instead of frequency density distorts the chart whenever class widths differ.

Reading a histogram

Working backwards from a histogram recovers frequencies.

Why this matters

Statistical diagrams are examined both as construction (draw the pie chart, complete the histogram) and as interpretation (read off a value, find a missing frequency), and they reward accurate scales and careful reading. The pie chart angle calculation and the histogram frequency-density idea are the two reliable mark-earners, and the histogram in particular is a Higher discriminator that catches candidates who plot frequency directly. Matching the right diagram to the data type also links back to classifying data in the sampling topic.

Exam-style practice questions

Practice questions written in the style of WJEC exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

WJEC 20193 marksIn a survey of 7272 people, 3030 chose tea, 2424 chose coffee and 1818 chose water. Work out the angle for tea in a pie chart. (Foundation and Higher, Unit 1, non-calculator.)
Show worked answer →

A full pie chart is 360∘360^\circ shared between 7272 people, so each person is worth 360∘÷72=5∘360^\circ \div 72 = 5^\circ.

Tea was chosen by 3030 people, so its angle is 30×5∘=150∘30 \times 5^\circ = 150^\circ.

Markers award a mark for the angle per person (5∘5^\circ), a mark for multiplying by the tea frequency and a mark for 150∘150^\circ. Dividing 360∘360^\circ by the number of categories instead of the total frequency is the usual error.

WJEC 20223 marksA histogram class 20<x≤4020 < x \le 40 has frequency 5050. Work out the frequency density for this class, and explain what the bar's height represents. (Higher, Unit 2, calculator.)
Show worked answer →

The class width is 40−20=2040 - 20 = 20.

Frequency density == frequency ÷\div class width =50÷20=2.5= 50 \div 20 = 2.5.

The height of a histogram bar is the frequency density, so the area of the bar (height times width) represents the frequency.

Markers give a mark for the class width, a mark for the frequency density 2.52.5, and a mark for explaining that area, not height, gives the frequency. Plotting frequency as the height is the classic histogram mistake.

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