POP

E9.4 Statistical Charts and Diagrams

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01 — Explanation

How do I choose the right diagram for a data set?

Chart	Best for	Key construction rule
Bar chart	Comparing categories	Equal-width bars, equal gaps
Pie chart	Proportions of a whole	Sector angle $=\dfrac{\text{category }f}{\text{total }f}\times360°$
Pictogram	Simple visual comparison	Key must state what each symbol (and partial symbol) represents
Stem-and-leaf	Exact values plus distribution shape	Data must be ordered, with a key

02 — Explanation

How do I calculate the angle for a pie chart sector?

Turn the category's share of the total into a fraction, then scale it up to $360°$ .

Example: $40$ students chose a favourite subject — Maths ( $14$ ), Science ( $10$ ), English ( $8$ ), Art ( $8$ ). The Maths sector:

\theta = \frac{14}{40}\times360° = 126°

Examiner Tip

After finding every sector angle, add them together as a check — a correctly calculated pie chart always sums to exactly $360°$ .

03 — Explanation

How do I work backwards from a pie chart to find a frequency?

Given a sector's angle rather than its frequency, the same fraction runs in reverse: the sector's share of $360°$ equals its share of the total frequency.

Example: in a pie chart of $180$ survey responses, the "Excellent" sector has an angle of $72°$ . Find how many people answered "Excellent."

\text{frequency} = \frac{72°}{360°}\times180 = 0.2 \times 180 = 36

This reverse calculation appears just as often in exams as finding the angle itself, so it's worth practising both directions rather than only the forward one.

04 — Explanation

How do I interpret a pictogram with partial symbols?

Each full symbol represents a fixed amount stated in the key, and a partial symbol represents a proportional fraction of that amount — a half-symbol is worth half the key value, not necessarily "roughly half" of it.

Example: a pictogram key states " $\text{🍎} = 8$ apples sold." A row showing $3$ full symbols and one half symbol represents $3\times8 + \frac12\times8 = 24+4=28$ apples sold that day.

05 — Explanation

How do I draw an ordered stem-and-leaf diagram?

Split each value into a "stem" (all digits except the last) and a "leaf" (the last digit), then list the leaves for each stem in ascending order.

Example: $23,31,45,22,38,40,29,33$

2 | 2 3 9
3 | 1 3 8
4 | 0 5

Key: $2\,|\,2$ represents $22$ .

Both the ordering and the key are required — a diagram with unsorted leaves, or no key at all, is not a complete answer even if every value is present.

06 — Explanation

What's the difference between a composite and a dual bar chart?

A composite (stacked) bar chart splits each bar into sections stacked on top of each other, showing the total and its breakdown together. A dual (side-by-side) bar chart places separate bars next to each other for each category, making direct comparison between them easier to read.

Examiner Tip

A pictogram is only ever as precise as its smallest drawn fraction of a symbol — if a key only uses whole and half symbols worth $8$ each, an exact value like $27$ simply cannot be shown, and the diagram can only communicate values in steps of $4$ at best.

07 — Explanation

When should I choose a stem-and-leaf diagram over a bar chart?

A bar chart groups data into categories and loses the individual values once drawn. A stem-and-leaf diagram keeps every original value visible while still showing the overall shape of the distribution at a glance — making it the better choice whenever a question specifically needs the exact data values preserved alongside a visual summary.