Cambridge IGCSE Mathematics 0580: Statistical charts and diagrams – Study Guide

This study guide covers Cambridge IGCSE Mathematics 0580, aligned to the Cambridge IGCSE Mathematics 0580 syllabus for exams in 2025, 2026 and 2027. It teaches syllabus section C9.4/E9.4 Statistical charts and diagrams in depth. The Core and Extended columns of the syllabus list exactly the same learning outcomes for 9.4, so everything on this page applies to both tiers and nothing here is Extended only.

For the whole of Topic 9, see the Statistics study guide. Reading tables and comparing data sets (9.1 and 9.2) are taught in the classifying and interpreting data guide.

What this subtopic covers

The syllabus says: “Draw and interpret” each of the five items below.

Syllabus ref	What you must be able to do	Tier
9.4 (a)	Draw and interpret bar charts, including composite (stacked) and dual (side-by-side) bar charts	Core and Extended
9.4 (b)	Draw and interpret pie charts	Core and Extended
9.4 (c)	Draw and interpret pictograms	Core and Extended
9.4 (d)	Draw and interpret stem-and-leaf diagrams, with ordered data and a key	Core and Extended
9.4 (e)	Draw and interpret simple frequency distributions	Core and Extended

Core candidates sit Paper 1 (non-calculator) and Paper 3 (calculator); Extended candidates sit Paper 2 (non-calculator) and Paper 4 (calculator). Practise the pie chart arithmetic by hand. The syllabus lists a ruler, compasses and a protractor for all papers.

9.4 (e) Simple frequency distributions

A frequency distribution shows each value (or class) and how often it occurs. A frequency table is the usual form; a bar chart is the usual picture of it.

Worked example 1. A survey recorded the number of people living in each of the flats in one building.

Number of people   1    2    3    4    5
Frequency          6   13    9    8    4

(a) How many flats are there? Add the frequencies: 6 + 13 + 9 + 8 + 4 = 40 flats.

(b) How many people live in the building? Each row gives value × frequency people.

1 × 6  =  6
2 × 13 = 26
3 × 9  = 27
4 × 8  = 32
5 × 4  = 20
Total  = 111 people

Do not add the top row (1 + 2 + 3 + 4 + 5 = 15). That is meaningless.

(c) What fraction of the flats have more than 2 people? 9 + 8 + 4 = 21, so 21/40. “More than 2” does not include 2.

(d) Draw the distribution as a bar chart. Here each █ is one flat.

Number of people
1  ██████              6
2  █████████████      13
3  █████████           9
4  ████████            8
5  ████                4
   0    5    10   15
         Frequency

On paper you would usually draw vertical bars. The data are discrete, so the bars are separate, with equal gaps.

9.4 (a) Bar charts

Drawing a bar chart

• Label both axes, start the frequency axis at 0 and use an even scale.
• Make every bar the same width; the height shows the frequency.
• Leave equal gaps between bars for categories or discrete values.

Composite (stacked) bar charts

A composite bar chart has one bar for each group, split into sections. The full height of the bar is the group total. Each section is one category.

Worked example 2. Students in three year groups were asked to choose one lunch option.

           Hot meal   Sandwich   Packed lunch   Total
Year 9        40         25           15          80
Year 10       35         30           25          90
Year 11       20         40           30          90

To draw the stacked bar for Year 9, find the running totals: hot meal from 0 to 40, sandwich from 40 to 65 (40 + 25), packed lunch from 65 to 80 (65 + 15). Do the same for the other years.

Key: █ hot meal   ▒ sandwich   ░ packed lunch     (each block = 5 students)

Year 9   ████████▒▒▒▒▒░░░                     80
Year 10  ███████▒▒▒▒▒▒░░░░░                   90
Year 11  ████▒▒▒▒▒▒▒▒░░░░░░                   90

• Each section’s value is end minus start (top minus bottom on a vertical chart). For Year 11, packed lunch runs from 60 to 90, so it is 90 − 60 = 30 students. Reading off “90” is the classic error.
• The whole bar gives the total, so Year 10 and Year 11 have the same number of students (90).
• Fractions come from the bar total. Half of Year 9 chose a hot meal, since 40/80 = 1/2. One third of Year 11 brought a packed lunch, since 30/90 = 1/3.

Dual (side-by-side) bar charts

A dual bar chart puts the bars for each category next to each other, all starting from 0, with a key. Here is the same lunch data drawn by option instead of by year.

Key: Y9 = Year 9, Y10 = Year 10, Y11 = Year 11     (each block = 5 students)

Hot meal       Y9   ████████           40
               Y10  ███████            35
               Y11  ████               20
Sandwich       Y9   █████              25
               Y10  ██████             30
               Y11  ████████           40
Packed lunch   Y9   ███                15
               Y10  █████              25
               Y11  ██████             30

Which bar chart to use

• A dual chart is better for comparing one category across groups, because every bar starts at 0. It shows at once that sandwiches become more popular from Year 9 to Year 11 (25, 30, 40) while hot meals become less popular (40, 35, 20).
• A composite chart is better for comparing totals and the make-up of each total, because the full bar is the total.

9.4 (c) Pictograms

A pictogram uses a symbol to stand for a fixed number of items. The key gives that number. A part of a symbol stands for the same fraction of the number.

Worked example 3. A pictogram shows the number of books borrowed from a school library on five days. The key is ● = 8 books. A quarter symbol ◔ is 2 books, a half ◑ is 4 and three quarters ◕ is 6.

Monday      ● ● ● ◑
Tuesday     ● ● ◔
Wednesday   ● ● ● ●
Thursday    (not yet drawn)
Friday      ● ◕
Key: ● = 8 books

(a) Read the known days.

Monday     3½ × 8 = 28
Tuesday    2¼ × 8 = 18
Wednesday  4  × 8 = 32
Friday     1¾ × 8 = 14

(b) The total for the week was 130 books. Complete Thursday.

Known days: 28 + 18 + 32 + 14 = 92
Thursday:   130 − 92 = 38 books
Symbols:    38 ÷ 8 = 4.75 = 4¾

So Thursday is drawn as ● ● ● ● ◕.

(c) How many more books were borrowed on Wednesday than on Tuesday? 32 − 18 = 14 books. Work with the numbers, not with counting symbols, so that the parts are handled correctly.

When you draw a pictogram, keep every symbol the same size and lined up, and always include the key.

9.4 (b) Pie charts

A pie chart shows how a whole is shared between categories. The angle of each sector is proportional to its frequency, and the angles add up to 360°.

Drawing a pie chart

angle for one item  = 360° ÷ total frequency
angle of a sector   = frequency × angle for one item

Worked example 4. 72 people were asked their favourite type of holiday.

Type        Frequency   Angle
Beach          26       26 × 5 = 130°
City           18       18 × 5 =  90°
Mountains      12       12 × 5 =  60°
Cruise          4        4 × 5 =  20°
Other          12       12 × 5 =  60°
Total          72                 360°

Step 1. Total frequency = 72, so one person is 360° ÷ 72 = 5°.

Step 2. Multiply each frequency by 5°, as in the table.

Step 3. Check the angles add to 360°: 130 + 90 + 60 + 20 + 60 = 360.

Step 4. Draw a circle with compasses and a radius from the centre. Measure each angle with a protractor from the previous line, in turn, and label each sector with the category (not only the angle).

Reading a pie chart

To get a frequency from a pie chart you need one link between angle and frequency: the total, or one category’s frequency.

Worked example 5. A pie chart shows the languages chosen by the students in one year group. French has an angle of 140°, Spanish 100° and Mandarin 48°. The only other sector is German. 75 students chose Spanish.

(a) Find the angle for German. 360 − 140 − 100 − 48 = 72°.

(b) Find the number of students in the year group.

100° stands for 75 students
1° stands for 75 ÷ 100 = 0.75 students
360° stands for 360 × 0.75 = 270 students

(c) Find the number who chose each other language.

French    140 × 0.75 = 105
German     72 × 0.75 =  54
Mandarin   48 × 0.75 =  36
Check: 105 + 75 + 54 + 36 = 270

Comparing two pie charts

A pie chart shows proportions, not sizes. Suppose a second school has 600 students in the same year, and its German sector is 60°. The angle is smaller than 72°, but the number is larger: 60/360 × 600 = 100 students, against 54 in the first school. You can say “a smaller proportion chose German”, but not “fewer students chose German”, unless you know both totals.

9.4 (d) Stem-and-leaf diagrams

A stem-and-leaf diagram keeps every data value while showing the shape of the data. The stem is the leading part of each value and the leaf is the final digit. The syllabus requires the data to be ordered and the diagram to have a key.

Worked example 6. The times, in seconds, of 20 students running 100 m were:

13.8  15.2  12.9  14.6  16.1  13.2  14.0  15.7  12.5  14.4
13.5  16.8  14.9  13.9  15.0  12.7  14.2  15.5  13.3  14.7

Step 1. Choose the stems: the whole seconds 12, 13, 14, 15 and 16. The leaf is the digit after the decimal point.

Step 2. Go through the list once, writing each leaf next to its stem (unordered).

12 | 9 5 7
13 | 8 2 5 9 3
14 | 6 0 4 9 2 7
15 | 2 7 0 5
16 | 1 8

Step 3. Count the leaves: 3 + 5 + 6 + 4 + 2 = 20, which matches the number of students.

Step 4. Redraw with the leaves in order and add the key.

12 | 5 7 9
13 | 2 3 5 8 9
14 | 0 2 4 6 7 9
15 | 0 2 5 7
16 | 1 8

Key: 12 | 5 means 12.5 seconds

Without the key, 12 | 5 could mean 125 or 1.25. The key fixes the place value.

Interpreting the diagram:

• Fastest and slowest: 12.5 s and 16.8 s, so the range is 16.8 − 12.5 = 4.3 s.
• Median: with 20 values, the median is halfway between the 10th and 11th. Count leaves from the top: the 10th is 14.2 and the 11th is 14.4, so the median is 14.3 s.
• Counting: 8 students ran under 14 seconds (all of rows 12 and 13). 6 students took 15 seconds or more, which is 6/20 = 3/10 of the group.
• Shape: the longest row is 14, so the most common times are 14.0 to 14.9 seconds.

Leaves are single digits, evenly spaced, with no commas.

Common errors

• Reading the end of a section on a composite bar chart instead of subtracting the value where it starts.
• Forgetting the key on a pictogram or stem-and-leaf diagram, so values are out by a factor or by a power of 10.
• Pie chart angles that do not add to 360°, caused by rounding or by a wrong total. Always check the sum.
• Saying more people chose a category because its sector is bigger, when the two pie charts have different totals.
• Leaving a stem-and-leaf diagram unordered, or finding the median by counting stems instead of leaves.
• Adding the values in the top row of a frequency table instead of the frequencies, or forgetting to multiply value by frequency when finding a total.
• Bar charts with unequal bar widths or a frequency axis that does not start at 0.

Next steps

• Statistics study guide and Statistics revision notes
• Statistics practice questions and Statistics and Probability (Extended) practice questions
• Check where you stand with the Core diagnostic or the Extended diagnostic
• All Cambridge IGCSE Mathematics resources: course hub
• Tick off every learning outcome with the printable checklist

Official syllabus

Cambridge International, Cambridge IGCSE Mathematics 0580 syllabus for exams in 2025, 2026 and 2027 (Version 3), Subject content, Topic 9 Statistics: C9.4/E9.4 Statistical charts and diagrams.