Draw and interpret statistical charts including bar charts, pie charts, frequency polygons, stem-and-leaf diagrams, box plots and histograms with unequal class widths (histograms at Higher tier).

What this dot point is asking

OCR references S2 and S3 cover drawing and interpreting statistical charts: bar charts, pie charts, frequency polygons, stem-and-leaf diagrams, box plots and, at Higher tier, histograms with unequal class widths. Each chart suits a particular kind of data and question. This content appears on every tier, and the histogram with frequency density is a signature Higher-tier topic that is frequently misread.

Bar charts and pie charts

These two charts handle categorical and proportional data.

So to draw a pie chart, find the angle for each category as $\dfrac{\text{frequency}}{\text{total}} \times 360^\circ$. To read one, reverse it: a $90^\circ$ sector is a quarter of the total. Bar charts are best for comparing actual frequencies, while pie charts are best for comparing proportions of a whole.

Frequency polygons, stem-and-leaf and box plots

Three further displays suit numerical data.

A frequency polygon plots the frequency against the midpoint of each class and joins the points with straight lines, showing the shape of a distribution and allowing two distributions to be compared on one diagram. A stem-and-leaf diagram splits each value into a stem (the leading digits) and a leaf (the last digit), keeping the actual data while revealing its shape, and a key is essential. A box plot (box-and-whisker) displays the five-number summary: minimum, lower quartile, median, upper quartile and maximum, making the median and interquartile range easy to read and compare.

Histograms (Higher)

A histogram is the key Higher-tier chart for grouped data with unequal class widths.

Histograms differ from bar charts in two ways: the bars touch (the data is continuous), and the area, not the height, represents frequency. This is essential when classes have unequal widths, because a wide class with a modest frequency should not tower over a narrow class. Reading "frequency density" as "frequency" is the single most common histogram error.

Why charts matter

Choosing and reading the right chart is a core data-handling skill, and OCR sets interpretation questions ("compare", "estimate", "what does this show?") that reward AO2 communication. The pie-chart angle method, the box-plot five-number summary and the histogram frequency-density rule are the most-tested techniques. Remembering that a histogram represents frequency by area, not height, is the key to the Higher-tier marks.