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EnglandMathsSyllabus dot point

How do you draw and interpret statistical charts and graphs?

Drawing and interpreting bar charts, pie charts, frequency tables, and cumulative frequency graphs, box plots and histograms at Higher tier.

A focused answer to the AQA GCSE Mathematics statistics content on charts and graphs, covering bar charts, pie charts and frequency tables, and cumulative frequency graphs, box plots and histograms at Higher tier.

Generated by Claude Opus 4.89 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 and pie charts
  3. Cumulative frequency graphs at Higher tier
  4. Box plots
  5. Histograms with unequal class widths
  6. Other displays and choosing the right one
  7. Misleading graphs

What this dot point is asking

AQA wants you to draw and interpret the standard statistical displays (bar charts, pie charts, frequency tables) and at Higher tier the more advanced ones (cumulative frequency graphs, box plots, and histograms with unequal class widths). The biggest Higher-tier trap is the histogram, where the vertical axis is frequency density, not frequency. Reading values off and comparing distributions are the key interpretation skills.

Bar charts and pie charts

A bar chart represents frequencies by the height of separate bars, with gaps between them for discrete categories. To draw a pie chart, work out the angle for each category as its frequency divided by the total, multiplied by 360∘360^\circ. The quick route is the angle per item: 360∘total\dfrac{360^\circ}{\text{total}}, then multiply by each frequency. Reading a pie chart in reverse, a sector of 90∘90^\circ represents a quarter of the total.

Cumulative frequency graphs at Higher tier

A cumulative frequency graph plots the running total of frequencies against the upper boundary of each class, then joins the points with a smooth curve. It is the main tool for reading the median and quartiles of grouped data.

Box plots

A box plot (box-and-whisker diagram) shows five values: the minimum, lower quartile, median, upper quartile and maximum. The box spans the interquartile range with a line at the median; the whiskers reach to the minimum and maximum. Box plots make it easy to compare two distributions side by side: compare medians for the typical value and box widths (IQR) for the spread.

Histograms with unequal class widths

This is why a wide class with a modest frequency can have a short bar: the frequency is spread over a wide interval, giving a low density. Always work with area for histograms, never height alone.

Other displays and choosing the right one

The specification also covers frequency polygons (join the midpoints of grouped data with straight lines to show the shape of a distribution), stem-and-leaf diagrams (which keep the original data values while showing the spread), and two-way tables (which cross-classify by two categories). Part of the assessment is choosing an appropriate display for a given purpose: pie charts show proportions of a whole, bar charts compare separate categories, cumulative frequency graphs reveal medians and quartiles, and histograms handle continuous data with unequal classes. Picking the wrong display, or being asked to criticise one, is a common interpretation question.

Misleading graphs

Examiners like to test whether you can spot a misleading display. Common tricks are a vertical axis that does not start at zero (exaggerating differences between bars), unequal scale intervals, or a pie chart whose sectors do not match the stated figures. When asked to comment, identify the specific feature that distorts the impression and explain how it misleads. This critical-reading skill reflects how statistics are used (and misused) in the media, and it carries real marks in the data-handling questions.

Exam-style practice questions

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

AQA 20183 marksIn a survey of 9090 people, 3030 chose tea, 4545 chose coffee and 1515 chose juice. Work out the angle needed to represent coffee on a pie chart. (Foundation tier, Paper 1, non-calculator.)
Show worked answer →

The whole pie is 360∘360^\circ for 9090 people, so each person is 36090=4∘\dfrac{360}{90} = 4^\circ.

Coffee was chosen by 4545 people, so its angle is 45×4=180∘45 \times 4 = 180^\circ.

Markers reward finding the angle per person and multiplying. Dividing 360360 by the number of categories (33) instead of the total people is the standard error.

AQA 20214 marksA histogram has unequal class widths. One bar covers the interval 2020 to 3030 with a frequency density of 1.41.4, and another covers 3030 to 5050 with frequency density 0.80.8. Work out the total frequency across these two intervals. (Higher tier, Paper 2, calculator.)
Show worked answer →

Frequency equals frequency density times class width.

First bar: 1.4×10=141.4 \times 10 = 14. Second bar: 0.8×20=160.8 \times 20 = 16.

Total frequency: 14+16=3014 + 16 = 30.

Markers reward multiplying density by width for each bar and summing. Reading the density as the frequency directly (ignoring class width) is the classic mistake.

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