C9.4 Statistical charts and diagrams

Learning objectives

C9.4.1Draw 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 bar heights; in dual bars compare paired groups, and in composite bars compare both parts and totals
Pie chart	sector angle $=\dfrac{\text{frequency}}{\text{total}}\times360^\circ$	compare proportions; convert an 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 every row and give a key	recover the original values and read their distribution
Frequency distribution	list each value or category once with its frequency	check the total frequency and identify common or rare values

For bars, choose a linear scale that reaches 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 segment heights add to its total; read a segment from the difference between its two 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 $360^\circ$ , which checks 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 a stem-and-leaf diagram retains individual values. This objective uses simple frequency distributions; grouped-data estimates and scatter-diagram correlation belong elsewhere.

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