IGCSE · Practice questions · Statistical charts and diagrams

Pictures of data.

Six original Cambridge-style questions on drawing and interpreting bar charts, pictograms, pie charts and stem-and-leaf diagrams.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Use the key, and use 360° for the whole.

Pie chart angles: \(\dfrac{360^\circ}{\text{total}}\) per item, then check the angles add to \(360^\circ\).
Reading a pie chart: number \(= \dfrac{\text{angle}}{360} \times \text{total}\).
Pictograms: symbols \(\times\) key value; part-symbols are fractions of it.
Composite bars: section size = top reading \(-\) bottom reading.
Stem-and-leaf: ordered leaves and a key, every time.

Recall

[3 marks]

40 students chose their favourite sport: football 14, netball 10, hockey 9, tennis 7. Calculate the angle of each sector of a pie chart.

Each student is \(\dfrac{360^\circ}{40} = 9^\circ\). ✓
Football \(126^\circ\), netball \(90^\circ\), hockey \(81^\circ\), tennis \(63^\circ\). ✓
Check: \(126 + 90 + 81 + 63 = 360^\circ\). ✓

Calculation

[2 marks]

In a pie chart, a sector of \(54^\circ\) represents 27 people. (a) How many people does the whole pie chart represent? (b) How many people does a \(100^\circ\) sector represent?

(a) Each person is \(\dfrac{54}{27} = 2^\circ\), so the total is \(\dfrac{360}{2} = 180\) people. ✓
(b) \(\dfrac{100}{2} = 50\) people. ✓

Calculation

[3 marks]

The ages of 12 members of a club are

34 27 41 38 29 45 33 27 50 36 42 31

(a) Draw an ordered stem-and-leaf diagram with a key. (b) Find the median age.

(a) 2 | 7 7 9 3 | 1 3 4 6 8 4 | 1 2 5 5 | 0 with Key: 3 | 4 means 34 years. ✓
(b) \(n = 12\): the median is halfway between the 6th and 7th values, 34 and 36, so 35 years. ✓

Analysis

[2 marks]

In a composite bar chart, the bar for one shop reaches 60 sales. The sections are: phones from 0 to 25, tablets from 25 to 48, laptops from 48 to 60. How many more tablets than laptops were sold?

Tablets: \(48 - 25 = 23\). Laptops: \(60 - 48 = 12\). ✓
\(23 - 12 = 11\) more tablets. ✓

Analysis

[2 marks]

In a pictogram, one symbol represents 12 visitors. (a) How many symbols should be drawn for 30 visitors? (b) How many visitors do \(4\tfrac{1}{4}\) symbols represent?

(a) \(\dfrac{30}{12} = 2.5\), so two and a half symbols. ✓
(b) \(4.25 \times 12 = 51\) visitors. ✓

Analysis

[4 marks]

180 people were asked how they travel to work. The pie chart has a \(150^\circ\) sector for bus and a \(90^\circ\) sector for car. The rest travel by cycle or on foot, and the angle for cycle is twice the angle for walk.

(a) Find the angle for walk. (b) How many people cycle?

(a) Angles left: \(360 - 150 - 90 = 120^\circ\). Walk \(= x\), cycle \(= 2x\), so \(3x = 120\) and \(x = 40^\circ\). ✓
(b) Cycle angle \(= 80^\circ\). Each person is \(\dfrac{360}{180} = 2^\circ\), so \(\dfrac{80}{2} = 40\) people cycle. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.