Bar charts, pictograms, pie charts and stem-and-leaf diagrams each show a frequency table as a picture. Drawing them accurately and reading them back are both exam skills, and pie charts need a little arithmetic with 360°.
In a pie chart the whole circle, \(360^\circ\), is the total frequency, so each item gets \(\dfrac{360^\circ}{\text{total}}\). In a pictogram, always use the key. A stem-and-leaf diagram must be ordered and must have a key.
Fig. 1: the favourite fruit of 60 people (Apple 18, Banana 12, Orange 20, Grapes 10) as a bar chart and as a pie chart, both drawn to scale. Each person is worth 360° ÷ 60 = 6° of the pie.
Section 01
Bar charts and pictograms.
In the lab's charts tab, change the numbers of each fruit and watch the bar chart, the pictogram and the pie chart all redraw from the same table. Switch to the dual and composite bar charts and compare how they show two groups.
Bar chart: bars of equal width with equal gaps; the height is the frequency. Label both axes and use a linear scale starting at 0.
Dual bar chart: two bars side by side for each category (for example boys and girls), with a key.
Composite (stacked) bar chart: one bar per group split into sections. The size of a section is the DIFFERENCE between its top and bottom readings.
Pictogram: each symbol stands for a fixed number given in the key; part-symbols stand for fractions of it.
Worked example Read a pictogram
In a pictogram, one circle represents 4 books. Ali has 3 and a half circles, and Bea has 2 and a quarter circles. How many more books did Ali read than Bea?
Ali: \(3.5 \times 4 = 14\) books.
Bea: \(2.25 \times 4 = 9\) books.
Difference: \(14 - 9 = 5\) books.
Answer: 5 books
Your turn
In a composite bar chart, the bar for Year 10 reaches 60 students. The 'walk' section goes from 0 to 25, 'bus' from 25 to 48 and 'car' from 48 to 60. How many Year 10 students travel by bus?
The bus section is from 25 to 48, so \(48 - 25 = 23\) students (not 48).
Examiner trap
In a composite bar chart, read the size of each section, not the height of its top. The bus section that ends at 48 is \(48 - 25 = 23\) students.
Section 02
Pie charts and 360°.
A pie chart shows how a whole is shared out. Find the angle for one item first, then multiply. To read a pie chart, go the other way: angle \(\div\) angle per item.
Worked example Draw a pie chart
60 people chose their favourite fruit: Apple 18, Banana 12, Orange 20, Grapes 10. Calculate the angles for a pie chart.
Each person gets \(\dfrac{360^\circ}{60} = 6^\circ\).
In a pie chart, the sector for 'cycle' has angle \(72^\circ\) and represents 30 people. (a) How many people are in the survey? (b) How many people does a \(48^\circ\) sector represent?
(a) \(72^\circ\) is \(\dfrac{72}{360} = \dfrac{1}{5}\) of the circle, so the total is \(30 \times 5 = 150\) people.
(b) Each person is \(\dfrac{360^\circ}{150} = 2.4^\circ\), so \(48^\circ\) is \(\dfrac{48}{2.4} = 20\) people.
Answer: (a) 150 (b) 20
Examiner trap
A bigger angle does not always mean more people when two pie charts have different totals. \(80^\circ\) of 72 people and \(64^\circ\) of 90 people are both 16 people.
Stage 1 · Learn
Check your understanding
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Quick check+10 XP
A pie chart shows 90 people. How many degrees represent one person?
Quick check+10 XP
In a stem-and-leaf diagram the key is 5 | 2 = 52. What does the leaf 7 on stem 4 represent?
Quick check+10 XP
Which chart shows the results for boys and girls as two bars side by side?
Quick check+10 XP
In a pictogram one symbol represents 10 people. How many people does half a symbol represent?
Section 03
Stem-and-leaf diagrams.
Open the stem-and-leaf tab: the stem is the tens digit and the leaf is the units digit. Type in your own numbers and watch them sort themselves onto the stems. Unlike a bar chart, the diagram keeps every value, so you can still find the median and range.
Worked example Build and use a stem-and-leaf diagram
The pulse rates of 15 people are 63, 51, 78, 45, 58, 63, 42, 69, 50, 64, 71, 56, 51, 47, 63. Draw an ordered stem-and-leaf diagram, then find the median, mode and range.
Stems 4, 5, 6, 7. Put each units digit on its stem, then ORDER each row.
4
2 5 7
5
0 1 1 6 8
6
3 3 3 4 9
7
1 8
Key: 5 | 1 means 51 beats per minute.
\(n = 15\), so the median is the 8th value: 42, 45, 47, 50, 51, 51, 56, 58.
No key, no marks: the examiner must know whether 5 | 1 means 51, 5.1 or 510. And an unordered stem-and-leaf diagram also loses a mark.
Stage 2 · Exam
Exam-style questions
Unlocks once the four checks above are done. Worth more XP, written to IGCSE Paper 2 and Paper 4 standard.
Finish the four checks above to unlock the exam questions
Exam style+20 XP
240 students were asked how they travel to school. In a pie chart, the sector for bus has angle \(105^\circ\). How many students travel by bus?
Exam style+20 XP
In a pictogram, one symbol represents 8 cars. Monday shows \(3\tfrac{1}{2}\) symbols and Tuesday shows \(2\tfrac{3}{4}\) symbols. How many more cars were there on Monday than on Tuesday?
Exam style+20 XP
1
5 8
2
0 3 3 7 9
3
1 4 4 4 6
4
2 5 8
Key: 3 | 4 means 34. Find the median.
Exam style+20 XP
Pie chart A shows 72 people, with a tennis sector of \(80^\circ\). Pie chart B shows 90 people, with a tennis sector of \(64^\circ\). Which group has more people who chose tennis?
Skill unlocked
Charts drawn and read.
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