What are the common methods of analysing data in Cambridge IGCSE Mathematics?

In Cambridge IGCSE Mathematics, common methods of analysing data include measures of central tendency (mean, median, mode), measures of dispersion (range, interquartile range, standard deviation), and graphical representations such as histograms, bar charts, and pie charts. These methods help in summarizing and interpreting data effectively.

How do you calculate the mean, median, and mode in a data set?

To calculate the mean, add all the numbers in the data set and divide by the number of values. The median is the middle value when the data is arranged in order, or the average of the two middle values if there is an even number of data points. The mode is the value that appears most frequently in the data set.

What is the importance of using graphical methods in data analysis?

Graphical methods, such as histograms, bar charts, and pie charts, are important in data analysis because they provide a visual representation of data, making it easier to identify patterns, trends, and outliers. These methods are particularly useful in Cambridge IGCSE Mathematics for interpreting and presenting data clearly and effectively.

How do you interpret the range and interquartile range in data analysis?

The range is the difference between the highest and lowest values in a data set, providing a basic measure of dispersion. The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1), representing the spread of the middle 50% of the data. In Cambridge IGCSE Mathematics, these measures help in understanding the variability and consistency of data.

Why is standard deviation an important measure in data analysis?

Standard deviation is important because it quantifies the amount of variation or dispersion in a data set. A low standard deviation indicates that data points are close to the mean, while a high standard deviation suggests a wide spread around the mean. In Cambridge IGCSE Mathematics, understanding standard deviation helps in assessing the reliability and consistency of data.

Why is "Forgetting to sort before finding the median" a common mistake in Methods of Analysing Data?

Why it happens: Speed. How to avoid it: Always sort the list ascending before reading the middle.

Why is "Computing $\bar{x} = \sum fx / n$ instead of $\sum fx / \sum f$" a common mistake in Methods of Analysing Data?

Why it happens: Confusing n (total values) with the count of distinct values. How to avoid it: Denominator is f — total frequency — not the number of rows. Source: 0580/42 — recurring

Why is "Using class boundaries instead of midpoints in grouped data" a common mistake in Methods of Analysing Data?

Why it happens: Picking the lower bound as x. How to avoid it: Class [10, 20) has midpoint 10 + 20/2 = 15.

Why is "Calling the grouped-data mean 'exact'" a common mistake in Methods of Analysing Data?

Why it happens: Forgetting the original values are lost. How to avoid it: Always say ESTIMATED mean.

StatisticsCambridge IGCSE Mathematics (0580)

Methods of Analysing Data

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

PreviousNext

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Study Notes

Full prose, callouts and a recap — built for A* mastery, not just a quick scan.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Methods of Analysing Data, ready to print or save offline.

Mean, Median, Mode and Range — Cambridge IGCSE 0580 Maths Extended (2026)

The four statistics every Cambridge candidate must compute fluently — for raw lists, frequency tables, and grouped data. Cambridge wants the right method AND the right interpretation.

What you’ll learn

Mapped to the Cambridge IGCSE 0580 syllabus (2025-2027).

E11.1 — Calculate the mean, median, mode and range for individual data.
E11.2 — Calculate an estimate of the mean for grouped data.
E11.3 — Identify the modal class from a grouped frequency distribution.

Mean, median, mode, range — raw data

Mean: sum/count. Median: middle when sorted. Mode: most common. Range: max - min.

Mean. Add up all the values, divide by how many there are. $\bar{x} = \dfrac{\sum x}{n}.$

Median. Sort the values from low to high. The median is the middle.

$n$ ODD: median is the $\dfrac{n+1}{2}$ -th value.
$n$ EVEN: median is the average of the $\dfrac{n}{2}$ -th and $(\dfrac{n}{2} + 1)$ -th values.

Mode. The value(s) that occur most often. A data set can be:

Unimodal: one mode.
Bimodal: two values tied for highest frequency.
No mode: every value occurs the same number of times.

Range. Maximum minus minimum.

Worked. Data: $4, 7, 2, 9, 4, 5, 8$ .

Sort: $2, 4, 4, 5, 7, 8, 9$ .
$n = 7$ , median = $\dfrac{8}{2} = 4$ th value = $5$ .
Mean: $\dfrac{2 + 4 + 4 + 5 + 7 + 8 + 9}{7} = \dfrac{39}{7} \approx 5.57$ .
Mode: $4$ (appears twice).
Range: $9 - 2 = 7$ .

Mean = sum / count.
Median: sort, find the middle.
Mode: most common.
Range: max $-$ min.
$n$ even: median is the average of the two middles.

Mean from a frequency table

$\bar{x} = \dfrac{\sum f x}{\sum f}$ . Multiply each value by its frequency.

When data is summarised in a frequency table: $\bar{x} = \dfrac{\sum f x}{\sum f}.$

Worked. Number of pets per household:

Pets ( $x$ )	Frequency ( $f$ )
0	5
1	12
2	8
3	3
4	2

$\sum f = 5 + 12 + 8 + 3 + 2 = 30$ .
$\sum f x = (0)(5) + (1)(12) + (2)(8) + (3)(3) + (4)(2) = 0 + 12 + 16 + 9 + 8 = 45$ .
Mean: $\dfrac{45}{30} = 1.5$ pets per household.

Median from a frequency table. Find the cumulative frequency. Locate the value at position $\dfrac{n+1}{2}$ (or the average of $\dfrac{n}{2}$ and $\dfrac{n}{2}+1$ for $n$ even). Use the cumulative column to find which $x$ value sits there.

Mode from a frequency table. The value with the highest frequency.

Mean: $\dfrac{\sum f x}{\sum f}$ .
Use cumulative frequency to find the median.
Mode: highest-frequency value.
Set up an extra column $f x$ for clarity.

Estimating the mean for grouped data

Use the MIDPOINT of each class as $x$ . The result is an ESTIMATE — the original values are unknown.

When data is grouped into class intervals (e.g. $0 < t \le 10$ , $10 < t \le 20$ , …) we don't know the exact values within each class. We approximate by assuming each value sits at the midpoint.

Steps.

Find the midpoint of each class: $x = \dfrac{\text{lower} + \text{upper}}{2}$ .
Compute $f x$ for each row.
Estimate of mean: $\dfrac{\sum f x}{\sum f}$ .

Worked. Time spent on homework (minutes):

Class	Midpoint $x$	Frequency $f$	$f x$
$0 < t \le 30$	15	4	60
$30 < t \le 60$	45	12	540
$60 < t \le 90$	75	8	600
$90 < t \le 120$	105	6	630

$\sum f = 30$ , $\sum f x = 1830$ .
Estimate of mean: $\dfrac{1830}{30} = 61$ minutes.

Why "estimate"? We assumed every value in $0 < t \le 30$ was exactly $15$ — usually false. The result is an APPROXIMATION.

Modal class. The class with the HIGHEST frequency. Cambridge expects you to write the full class interval (e.g. " $30 < t \le 60$ "), not just the midpoint.

Midpoint as the $x$ value.
Estimate of mean: $\dfrac{\sum f x}{\sum f}$ .
Modal class: highest-frequency interval.
Always write 'estimate' for grouped data.

Comparing data sets

Compare AVERAGES (mean / median) and SPREADS (range / IQR) — Cambridge wants both.

When asked to compare two data sets, Cambridge wants comments on TWO aspects:

1. Average / centre. Use mean or median.

Higher mean: data set is on average higher.
Outliers can pull the mean — median is more robust.

2. Spread / consistency. Use range or interquartile range (IQR — see Cumulative Frequency).

Smaller range: more consistent / less variable.
Smaller IQR: middle 50% is more tightly grouped.

Worked. Two classes' test scores:

Class A: mean $= 65$ , range $= 30$ .
Class B: mean $= 65$ , range $= 12$ .

Comment: "Both classes have the same mean ( $65$ ), so on average they performed equally. However, Class B has a much smaller range ( $12$ vs $30$ ), meaning Class B's scores are more consistent."

Cambridge mark scheme expectation. TWO comparison statements: one about average, one about spread. Each must reference the actual numerical statistics — vague statements like "Class B is more consistent" without citing the smaller range lose marks.

Compare TWO things: average AND spread.
Average: mean or median.
Spread: range or IQR.
Cite the actual statistics, not just descriptions.

How it’s examined

Statistics appears every Paper 2 (3-4 marks) and Paper 4 (5-7 marks). Cambridge typically combines a frequency-table mean with a comparison or interpretation question. Examiner reports flag two errors: (i) midpoints not used for grouped data, (ii) only one comparison statement (average without spread, or vice versa) when two are required.

Sources: Cambridge IGCSE Mathematics 0580 syllabus 2025-2027 (E11.1-11.3); 0580/22 May/Jun 2024 — Q11 (mean from frequency table); 0580 Examiner Reports 2022-2024. Last reviewed 2026-05-05.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Methods of Analysing Data, ready to print or save as PDF.

Step-by-step worked examples — Methods of Analysing Data

Step-by-step solutions to past-paper-style questions on methods of analysing data, written exactly the way a tutor would explain them at the board.

1Mean, median, mode and range
Core• averages
Question
Find the mean, median, mode and range of: $4, 6, 7, 7, 9, 12$ .
Step-by-step solution
1. Step 1
  Mean.
  $\bar{x} = \dfrac{4+6+7+7+9+12}{6} = \dfrac{45}{6} = 7.5$
2. Step 2
  Median (already sorted, $n = 6$ → average of middle two).
  $\text{Median} = \dfrac{7 + 7}{2} = 7$
3. Step 3
  Mode (most frequent).
  $\text{Mode} = 7$
4. Step 4
  Range.
  $\text{Range} = 12 - 4 = 8$
Answer
Mean $7.5$ , median $7$ , mode $7$ , range $8$ .
2Mean from a frequency table
Extended• frequency table
Question
Number of pets per household: $0$ (frequency $5$ ), $1$ (frequency $8$ ), $2$ (frequency $4$ ), $3$ (frequency $3$ ). Find the mean.
Step-by-step solution
1. Step 1
  $\bar{x} = \dfrac{\sum fx}{\sum f}$ .
  $\bar{x} = \dfrac{0(5) + 1(8) + 2(4) + 3(3)}{5+8+4+3} = \dfrac{0+8+8+9}{20} = \dfrac{25}{20}$
2. Step 2
  Compute.
  $= 1.25$
Answer
$1.25$ pets
3Estimated mean (grouped data)
Extended• Adapted from 0580/42 May/Jun 2024 Q10• grouped
Question
Times taken (minutes): $[10, 20)$ freq $4$ ; $[20, 30)$ freq $9$ ; $[30, 40)$ freq $7$ . Estimate the mean.
Step-by-step solution
1. Step 1
  Use class midpoints.
  $x = 15, 25, 35$
2. Step 2
  $\bar{x} = \dfrac{\sum fx}{\sum f}$ .
  $\bar{x} = \dfrac{4(15) + 9(25) + 7(35)}{20} = \dfrac{60 + 225 + 245}{20}$
3. Step 3
  Compute.
  $= \dfrac{530}{20} = 26.5$
Answer
Estimated mean $\approx 26.5$ minutes.
Examiner tip
Always say 'ESTIMATED' mean for grouped data — exact values aren't known.
4Modal class
Extended• modal class
Question
Using the same grouped data, identify the modal class.
Step-by-step solution
1. Step 1
  Highest frequency among the classes is $9$ .
  $\text{Modal class} = [20, 30)$
Answer
$[20, 30)$

Key Formulae — Methods of Analysing Data

The formulae you need to memorise for methods of analysing data on the Cambridge IGCSE 0580 paper, with every variable defined in plain English and a note on when to use it.

Mean of a list
$\bar{x} = \dfrac{\sum x}{n}$
$n$
number of values
When to use
Raw lists of data.
Mean from a frequency table
$\bar{x} = \dfrac{\sum fx}{\sum f}$
$f$
frequency of each value
$x$
value (or class midpoint)
When to use
Frequency tables and (using midpoints) grouped data.
Median position
$\text{Position} = \dfrac{n + 1}{2}$
When to use
Find which (sorted) value is the median. If position is non-integer, average the two surrounding values.

Key Definitions and Keywords — Methods of Analysing Data

Definitions to memorise and the exact keywords mark schemes credit for methods of analysing data answers — sharpened from recent examiner reports for the 2026 0580 sitting.

Mean
Examiner keyword
Sum of values divided by the number of values; the arithmetic average.
Median
Examiner keyword
The middle value once data is sorted. Average the two middle values when $n$ is even.
Mode
Examiner keyword
The most frequent value. Multiple modes are possible; if all unique, no mode.
Range
Examiner keyword
Highest value minus lowest value.
Modal class
Examiner keyword
In grouped data, the class with the highest frequency.

Common Mistakes and Misconceptions — Methods of Analysing Data

The traps other students keep falling into on methods of analysing data questions — taken from recent Cambridge IGCSE 0580 examiner reports and mark schemes — and how to avoid them.

✕Forgetting to sort before finding the median
Why it happens
Speed.
How to avoid it
Always sort the list ascending before reading the middle.
✕Computing $\bar{x} = \sum fx / n$ instead of $\sum fx / \sum f$
0580/42 — recurring
Why it happens
Confusing $n$ (total values) with the count of distinct values.
How to avoid it
Denominator is $\sum f$ — total frequency — not the number of rows.
✕Using class boundaries instead of midpoints in grouped data
Why it happens
Picking the lower bound as $x$ .
How to avoid it
Class $[10, 20)$ has midpoint $\dfrac{10 + 20}{2} = 15$ .
✕Calling the grouped-data mean 'exact'
Why it happens
Forgetting the original values are lost.
How to avoid it
Always say ESTIMATED mean.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.