Cambridge IGCSE Maths (0580) · Revision notes · Topic 9 of 9

Cambridge IGCSE Maths 0580 Statistics Notes

Revision notes for topic 9, Statistics, of the Cambridge IGCSE Mathematics (0580) syllabus for exams in 2025, 2026 and 2027. Each of the 7 sub-topics lists what the syllabus asks, marked Core or Extended, with a short explanation and a worked example. Cover the answer and try each example first.

7 sub-topics
5 Core and Extended
2 Extended only
4 with notes written for 0580

Core Core students (Papers 1 and 3) learn the Core statements. Extended Extended students (Papers 2 and 4) learn everything: the Core statements, the Extended additions and the Extended-only sub-topics. Papers 1 and 2 are non-calculator.

9.1 Classifying statistical data

Core C9.1 Extended E9.1

Classify and tabulate data: categorical, discrete and continuous

New for 0580: not in Edexcel 4MA1: Not taught in 4MA1 Higher.

Notes for 0580

Categorical (qualitative) data are words or categories, such as eye colour or favourite sport. Numerical (quantitative) data are numbers: discrete data can take only particular values and are usually counted (number of siblings, shoe size); continuous data can take any value in a range and are measured (height, time, mass).

Continuous data are grouped in classes written with inequalities, such as 150 ≤ h < 160, so that every value belongs to exactly one class.

Example (Core, non-calculator): Is each of these categorical, discrete or continuous? (a) the number of goals scored in a match (b) the time taken to run 100 m (c) the colour of a car (d) shoe size.

(a) Goals are counted: whole numbers only.
(b) Time is measured and can take any value.
(c) Colours are categories, not numbers.
(d) Shoe sizes take only particular values (such as 6, 6½, 7).

Answer: (a) discrete (b) continuous (c) categorical (d) discrete

Example (Core, non-calculator): Heights are grouped in the classes 150 ≤ h < 160 and 160 ≤ h < 170 (in cm). Which class does a height of 160 cm go in?

160 ≤ h includes 160, but h < 160 does not.

Answer: 160 ≤ h < 170

0580 practice questions

12 questions written for 0580 in the Statistics practice: 12 Core, all non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Is each type of data categorical, discrete or continuous?

(a) eye colour (b) the number of brothers and sisters a student has

Show the answer and mark scheme

B1 (a) categorical
B1 (b) discrete

Answer: (a) categorical (b) discrete

Practice question (Core, non-calculator, 3 marks):

A survey asks each student six questions. Is the data from each question categorical, discrete or continuous?

(a) the number of people in your home (b) the distance from your home to school (c) how you travel to school (d) your shoe size (e) the time you spend on homework each night (f) your favourite subject

Show the answer and mark scheme

B3 (a) discrete (b) continuous (c) categorical (d) discrete (e) continuous (f) categorical (B2 for 4 or 5 correct, B1 for 2 or 3 correct)

Answer: (a) discrete (b) continuous (c) categorical (d) discrete (e) continuous (f) categorical

9.2 Interpreting statistical data

Core C9.2 Extended E9.2

Read and draw conclusions from tables and statistical diagrams
Compare sets of data using tables, graphs and statistical measures
Know the limits of what the data shows

Partly in Edexcel 4MA1: 4MA1 practises the measures; comparing two data sets in words (average and spread, in context) is not practised on its own.

Notes for 0580

To compare two sets of data, make two comments: one about an average (the mean or median: which set is higher on average) and one about spread (the range at Core; the range or interquartile range at Extended: the smaller spread is more consistent). Always say what the numbers mean in the context of the question.

Be careful with conclusions: a small sample, or one that does not represent everyone, may not tell you about the whole population, and one extreme value can pull the mean and range a long way.

Example (Core, non-calculator): Class A's test scores have mean 62 and range 30. Class B's have mean 58 and range 12. Compare the two classes.

Average: 62 > 58, so class A scored higher on average.
Spread: 12 < 30, so class B's scores were more consistent.

Answer: Class A did better on average; class B's scores were more consistent

Example (Core, non-calculator): Team P scored 1, 3, 3, 4, 9 goals in five games and team Q scored 2, 3, 4, 4, 4. Compare the teams using the median and the range.

P: median 3, range 9 − 1 = 8.
Q: median 4, range 4 − 2 = 2.
Q has the higher median and a much smaller range. (P's mean is 4, above its median, because the 9 pulls it up; Q's mean is 3.4.)

Answer: Team Q scored more on average (median 4 against 3) and far more consistently (range 2 against 8)

0580 practice questions

12 questions written for 0580 in the Statistics practice: 12 Core, 8 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

The daily sales at two shops are recorded for a month. Shop A: mean 45, range 20. Shop B: mean 52, range 35.

(a) Which shop sells more on average?

(b) Which shop has more consistent sales? Give a reason.

Show the answer and mark scheme

B1 (a) Shop B (higher mean)
B1 (b) Shop A, because its range is smaller

Answer: (a) Shop B (b) Shop A (smaller range)

Practice question (Core, non-calculator, 3 marks):

The monthly pay, in dollars, of the five workers in a small company is:

1200, 1250, 1300, 1280, 6000

(a) Find the mean and the median.

(b) The manager says that the average pay is more than $\$2000$. Explain why the median is a better average to use here.

Show the answer and mark scheme

B1 (a) mean 2206
B1 (a) median 1280
B1 (b) the mean is raised by one very large value (6000); four of the five workers earn between 1200 and 1300, close to the median, and none of them earns near the mean

Answer: (a) mean $\$2206$, median $\$1280$ (b) the mean is distorted by the one large value

Edexcel 4MA1 notes: Statistical Measures
Practise the shared part (4MA1 questions): Mean, Median and Mode questions

9.3 Averages and measures of spread

Core C9.3 Extended E9.3

Core calls this sub-topic "Averages and range"; "Averages and measures of spread" is the Extended title.

Mean, median, mode and range of individual data and of data in a list or frequency table (not grouped); choosing the right average

Extended also: Quartiles and interquartile range of individual data; Estimated mean and modal class of grouped data.

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

Mean = total ÷ count. Median = middle when ordered. Mode = most common. Range = max − min.

Example: Median + range of −3, 4, 7, 1, −1, 9, 5.

Answer: Ordered: −3, −1, 1, 4, 5, 7, 9. Median = 4 (the 4th of 7 values). Range = 9 − (−3) = 12.

0580 practice questions

6 questions written for 0580 in the Statistics practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 3 marks):

Here are seven numbers: $4, \ 7, \ 2, \ 7, \ 9, \ 3, \ 5$

Find

(a) the mode (b) the median (c) the range.

Show the answer and mark scheme

B1 (a) 7
B1 (b) 5
B1 (c) 7

Answer: (a) $7$ (b) $5$ (c) $7$

Practice question (Core, non-calculator, 2 marks):

Find the mean of $12, \ 15, \ 9, \ 14$.

Show the answer and mark scheme

M1 50 ÷ 4
A1 12.5

Answer: $12.5$

Edexcel 4MA1 notes: Statistical Measures
Practise (4MA1 questions, same mathematics): Mean, Median and Mode questions

9.4 Statistical charts and diagrams

Core C9.4 Extended E9.4

Draw and interpret bar charts (including composite and dual), pie charts, pictograms, ordered stem-and-leaf diagrams with a key, and simple frequency distributions
Box-and-whisker plots are not on the syllabus (removed in 2025)

Partly in Edexcel 4MA1: Pictograms are not practised and 4MA1 does not examine stem-and-leaf diagrams. Box plots are off both syllabuses (lib/bank-scope.js bans them for cie0580 too).

Notes for 0580

A stem-and-leaf diagram keeps every value: the stem is the leading digit (or digits) and the leaf is the last digit, with the leaves in order and a key such as 2 | 3 = 23. Find the median by counting leaves to the middle value; the range is the largest minus the smallest.

A pictogram uses a symbol to stand for a number of items, given in a key; part of a symbol stands for that part of the number. In a pie chart, each angle is frequency ÷ total × 360°.

Example (Core, non-calculator): The times, in minutes, that 11 students took to finish a task were 12, 15, 21, 23, 23, 27, 30, 34, 38, 41, 45. Draw a stem-and-leaf diagram and find the median and the range.

Stems are the tens digits 1 to 4; each leaf is a units digit, in order (see the diagram).
There are 11 values, so the median is the 6th value.
Range = 45 − 12

Key: 2 | 1 means 21 minutes
1	2 5
2	1 3 3 7
3	0 4 8
4	1 5

Answer: Median 27 minutes; range 33 minutes

Example (Core, non-calculator): In a pictogram, one symbol stands for 8 cars. (a) How many cars do 3½ symbols stand for? (b) How many symbols are needed for 20 cars?

(a) 3 × 8 = 24, plus half of 8 = 4, gives 28.
(b) 20 ÷ 8 = 2.5

Answer: (a) 28 cars (b) 2½ symbols

0580 practice questions

14 questions written for 0580 in the Statistics practice: 14 Core, 10 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

In a pictogram, one symbol represents 6 hours of sunshine.

(a) Monday is shown by $2\frac{1}{2}$ symbols. How many hours of sunshine were there on Monday?

(b) Tuesday had 9 hours of sunshine. How many symbols are needed for Tuesday?

Show the answer and mark scheme

B1 (a) 15
B1 (b) 1½

Answer: (a) 15 hours (b) $1\frac{1}{2}$ symbols

Practice question (Core, calculator, 4 marks):

The ordered stem-and-leaf diagram shows the masses of 12 parcels.

\[\begin{array}{c|l} 3 & 8\ 9 \\ 4 & 1\ 3\ 3\ 6\ 8 \\ 5 & 0\ 2\ 4\ 7 \\ 6 & 1 \end{array} \qquad \text{Key: } 4 \mid 1 \text{ represents } 4.1 \text{ kg}\]

(a) Find the median mass.

(b) Find the range.

Show the answer and mark scheme

M1 (a) (4.6 + 4.8) ÷ 2
A1 (a) 4.7 kg
B1 (b) 2.3 kg
B1 (c) 33.3% (4 out of 12)

Answer: (a) 4.7 kg (b) 2.3 kg (c) $33.3\%$

Practise the shared part (4MA1 questions): Histograms and Cumulative Frequency questions

9.5 Scatter diagrams

Core C9.5 Extended E9.5

Draw and interpret scatter diagrams
Positive, negative and zero correlation
Draw, interpret and use a line of best fit by eye

New for 0580: not in Edexcel 4MA1: 4MA1 does not examine scatter graphs or correlation.

Notes for 0580

A scatter diagram plots pairs of values as points. Positive correlation: as one variable increases, the other tends to increase. Negative correlation: as one increases, the other tends to decrease. Zero (no) correlation: no pattern. Say how strong it is too: strong when the points lie close to a line, weak when they are spread out.

A line of best fit is a single ruled straight line drawn by eye across the whole of the data, with the points evenly spread on each side of it. Good practice (not a syllabus requirement): check that it passes through the mean point (mean of x, mean of y). Use the line to estimate values inside the range of the data; estimates outside the range (extrapolation) are unreliable. Correlation does not show that one variable causes the other.

Example (Core, non-calculator): Five students revised for 2, 4, 6, 8 and 10 hours and scored 15, 21, 24, 31 and 34 in a test. Describe the correlation. Then find the mean point, a useful check when drawing a line of best fit (good practice, not a syllabus requirement).

The scores go up as the hours go up, close to a straight line: strong positive correlation.
Mean hours = 30 ÷ 5 = 6
Mean score = 125 ÷ 5 = 25

Answer: Strong positive correlation; mean point (6, 25)

Example (Core, non-calculator): A line of best fit for these data passes through the mean point (6, 25) and has gradient 2.5. Estimate the score of a student who revised for 7 hours. Why should the line not be used for a student who revised for 20 hours?

7 hours is 1 hour more than 6, so the estimate is 25 + 2.5 × 1 = 27.5
20 hours is far outside the data (2 to 10 hours), so the pattern may not continue.

Answer: About 27.5 (so 27 or 28 marks); 20 hours is outside the range of the data, so that estimate would be unreliable

0580 practice questions

16 questions written for 0580 in the Statistics practice: 16 Core, 10 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 1 mark):

A scatter diagram shows that as the outside temperature increases, the number of hot drinks sold at a café decreases. What type of correlation does this show?

Show the answer and mark scheme

B1 negative

Answer: negative correlation

Practice question (Core, calculator, 4 marks):

A scatter diagram shows the ages, $x$ years, and the values, $y$ thousand dollars, of some cars of the same model. The line of best fit passes through $(1, 58)$ and $(9, 18)$.

(a) Find the equation of the line of best fit.

(b) Use it to estimate the value of a car that is 6 years old.

Show the answer and mark scheme

M1 (a) gradient (18 − 58)/(9 − 1) = −5
A1 (a) y = −5x + 63
B1 (b) 33 (thousand dollars)
B1 (c) 14 is outside the data range (it gives a negative value, −7)

Answer: (a) $y = -5x + 63$ (b) $\$33\,000$ (c) outside the range of the data; it gives a negative value

9.6 Cumulative frequency diagrams

Extended only E9.6

Extended: Draw and interpret cumulative frequency tables and diagrams; Estimate the median, percentiles, quartiles and interquartile range.

Same mathematics as Edexcel 4MA1.

Edexcel 4MA1 notes: Statistics and Probability (all notes)
Practise (4MA1 questions, same mathematics): Histograms and Cumulative Frequency questions

9.7 Histograms

Extended only E9.7

Extended: Draw and interpret histograms with equal and unequal class widths, using frequency density.

Same mathematics as Edexcel 4MA1.

Revise it

In a histogram the bar AREA shows the frequency: frequency density = frequency ÷ class width.

Example: A class 10 < x ≤ 25 has frequency 30. Find its frequency density.

Answer: 30 ÷ 15 = 2.

Edexcel 4MA1 notes: Histograms & Frequency Density
Practise (4MA1 questions, same mathematics): Histograms and Cumulative Frequency questions

Practise statistics

60 practice questions are written for 0580 on 9.1, 9.2, 9.3, 9.4, 9.5. For the 3 sub-topics that are the same mathematics in Edexcel 4MA1, the practice also has our 4MA1 Higher questions, which are Extended level. Core students: use the Core filter on the practice page; every sub-topic with Core content has questions written for 0580 Core. Practice is part of the IGCSE plan, with a free preview; these notes are free.

Statistics practice for 0580: the 60 questions written for 0580, tagged Core or Extended and non-calculator or calculator, with the Edexcel 4MA1 Higher questions for the sub-topics that are the same mathematics
Student hub: the Edexcel 4MA1 units (Unit 6), each question marked
Cambridge IGCSE Maths 0580 past papers: the 2025 specimen papers and past papers, with a timer
IGCSE Maths questions by topic with worked answers