E9.4 Statistical charts and diagrams

Learning objectives

E9.4.1Draw and interpret: (a) bar charts (b) pie charts (c) pictograms (d)• Draw and interpret: (a) bar charts (b) pie charts (c) pictograms (d) stem-and-leaf diagrams (e) simple frequency distributions. Includes composite (stacked) and dual (side-by- side) bar charts. Stem-and-leaf diagrams should have ordered data with a key.

A statistical display represents frequencies so that categories, proportions or the shape of individual data can be compared. A correct display preserves every frequency and uses a clear scale or key.

Display	Construction rule	What to interpret
Bar chart	equal-width bars, consistent gaps and a labelled linear frequency scale	compare heights; in dual bars compare paired groups, and in composite bars compare parts and totals
Pie chart	sector angle $=\dfrac{\text{frequency}}{\text{total}}\times360^\circ$	compare proportions; convert angle back with $\dfrac{\text{angle}}{360^\circ}\times\text{total}$
Pictogram	use one stated key for every symbol, including fractional symbols	multiply symbols by the key before comparing frequencies
Stem-and-leaf	split each value into a stem and leaf, order each row and give a key	recover original values and read their distribution
Frequency distribution	list each value or category once with its frequency	check total frequency and identify common or rare values

For bars, choose a linear scale reaching the largest frequency, label both axes and plot each height accurately. A dual bar chart needs a key and the same scale for both groups. A composite bar's segments add to its total; read a segment from the difference between its boundaries. Unequal widths or a non-linear unmarked scale are misleading.

For frequencies $9,14,7$ , the total is $30$ . The sector angles are $9\div30\times360^\circ=108^\circ$ , $14\div30\times360^\circ=168^\circ$ and $7\div30\times360^\circ=84^\circ$ . They sum to $360^\circ$ , checking the chart.

For $13,15,21,21,28,31$ , use stems $1,2,3$ and ordered leaves: $1\mid3\ 5$ , $2\mid1\ 1\ 8$ , $3\mid1$ . The key $1\mid3=13$ fixes the place value. Every original value must appear exactly once.

Interpret only what the display supports: read the scale and key before calculating, and compare like with like. Bars show frequencies, pie sectors show proportions, and stem-and-leaf retains individual values. Box plots, histograms and scatter diagrams belong to other frozen objectives.

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