Drawing and interpreting statistical diagrams: bar charts, pictograms, pie charts, frequency polygons, cumulative frequency graphs and box plots, and finding the median, quartiles and interquartile range (Higher tier).

What this dot point is asking

Edexcel expects you to draw and interpret a range of statistical diagrams, from bar charts and pie charts up to cumulative frequency graphs and box plots, and at Higher tier to find the median, quartiles and interquartile range. Each diagram suits a different kind of data, and reading values accurately from a graph is a frequent source of marks.

Bar charts, pictograms and pie charts

These diagrams display categorical or discrete data. A bar chart uses bars of equal width with heights showing frequency, leaving gaps between categories. A pictogram uses symbols, with a key stating how many each symbol represents. A pie chart shows each category as a "slice" whose angle is proportional to its frequency.

So if $45$ out of $180$ people prefer tea, the tea angle is $\dfrac{45}{180} \times 360^\circ = 90^\circ$. Reading a pie chart backwards, an angle of $90^\circ$ out of $360^\circ$ is a quarter of the total.

Frequency polygons

A frequency polygon shows the shape of grouped data by plotting the frequency against the midpoint of each class and joining the points with straight lines. It is useful for comparing two distributions on the same axes, because the overall shapes can be seen at a glance.

Cumulative frequency graphs (Higher)

Cumulative frequency is a running total, and its graph is the key to finding the median and quartiles of grouped data.

Box plots (Higher)

A box plot summarises a distribution using five numbers: the minimum, lower quartile, median, upper quartile and maximum. The box spans the interquartile range, with a line at the median, and "whiskers" reach to the minimum and maximum. Box plots are ideal for comparing two distributions: compare medians for typical values and interquartile ranges for spread.

Choosing the right diagram

Each diagram suits particular data, and a question may ask which is appropriate. Bar charts and pie charts suit categorical or discrete data, with pie charts best when you want to show proportions of a whole. Frequency polygons and cumulative frequency graphs suit grouped continuous data, the cumulative frequency graph being the route to the median and quartiles. Box plots are best for comparing the spread and centre of two or more data sets at a glance. Reading values accurately is where most marks are won or lost, so always use a ruler to read across and down from a graph, and state whether a value is exact or an estimate.

Try this

Q1. In a survey of $120$ people, $40$ chose blue. What angle represents blue on a pie chart? [2 marks]

• Cue. $\dfrac{40}{120} \times 360^\circ = 120^\circ$.

Q2. A data set has lower quartile $18$ and upper quartile $29$. Work out the interquartile range. [1 mark]

• Cue. $29 - 18 = 11$.