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C9.4 Statistical Charts and Diagrams

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01 — Explanation

How do I read and draw a bar chart?

Bars are of equal width, height proportional to frequency, with gaps between bars. A composite (stacked) bar chart stacks sub-categories within a single bar; a dual (side-by-side) bar chart places bars for two data sets next to each other for direct comparison.

Common mistake

drawing bars touching each other. Bars only touch in a histogram, which is an Extended-tier topic — Core bar charts always need equal gaps between every bar, regardless of how many categories or sub-categories are shown.

Worked example. A dual bar chart shows the number of hours of sunshine in June and July across four cities. If City A had 180 hours in June and 210 hours in July, describe how this would appear on the chart.

Two bars would be drawn side-by-side for City A, both of equal width: the June bar reaching a height of $180$ on the frequency axis, and the July bar (placed immediately next to it) reaching $210$ — taller than the June bar, making the increase visually obvious at a glance.

02 — Explanation

How do I calculate the angle in a pie chart?

\text{sector angle} = \frac{\text{category frequency}}{\text{total frequency}}\times 360^\circ

Worked example. A survey of 90 students' favourite pets gives Dog: 36, Cat: 27, Other: 27. Find the sector angle for "Dog."

\frac{36}{90} = 0.4 \qquad 0.4\times360^\circ = 144^\circ

Exam tip

don't stop at the decimal or percentage — always convert all the way through to degrees out of $360^\circ$ . As a check, the sector angles for every category in a pie chart must always add up to exactly $360^\circ$ .

03 — Explanation

How do I use a pictogram?

A pictogram uses repeated symbols to represent frequency, with a key showing what a full or partial symbol stands for.

Worked example. A pictogram's key states that $\bigstar$ represents $4$ books. One row shows $2\tfrac{1}{2}$ stars. Find the frequency this row represents.

2.5\times4 = 10 \text{ books}

Common mistake

treating a half-symbol as always meaning "half of one unit" (e.g. $0.5$ ) rather than half of whatever the key actually represents. Always read the key's value first, then scale it by the fraction of symbol shown.

04 — Explanation

How do I read a stem-and-leaf diagram?

Each value splits into a "stem" (leading digit) and "leaf" (final digit); leaves must be ordered, and a key must be given, e.g. $3\mid4$ means $34$ .

Worked example.

\begin{array}{c|l} 1 & 2\ 5\ 8 \\ 2 & 0\ 3\ 3\ 7 \\ 3 & 1\ 4 \end{array} \quad \text{Key: } 1\mid2=12

State the number of values recorded, and find the mode.

Counting every leaf: $3+4+2=9$ values. The leaf $3$ appears twice in the " $2$ " row, giving $23$ twice — no other value repeats, so the mode is $23$ .

Common mistake

omitting the key. A stem-and-leaf diagram is meaningless without one, and leaves within each row must be ordered smallest to largest before the diagram is considered complete.

05 — Explanation

What is a simple frequency distribution, and how does it differ from these other charts?

A frequency distribution is simply a list or table pairing each value (or category) with how often it occurs — every chart above is really just a different visual way of displaying one. Recognising which chart best suits a given data set is as important as being able to draw each one correctly: categorical data (like favourite colour) suits a bar chart or pie chart, while numerical data with many different values suits a stem-and-leaf diagram, which preserves every individual value instead of grouping them into bars.

Worked example. A frequency table shows the number of goals scored by a football team in 10 matches: $0$ goals in $2$ matches, $1$ goal in $3$ matches, $2$ goals in $4$ matches, $3$ goals in $1$ match. State which chart type would represent this data most clearly, and explain why.

A bar chart is most suitable, since "number of goals" is discrete numerical data with only a few distinct values — a bar chart, with one gapped bar per goal-value and height equal to frequency, shows the shape of this distribution far more clearly than a stem-and-leaf diagram would for such a small range of values.