Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Methods of Analysing Data — calculating and interpreting averages and spread from raw and grouped data — to become a reliable source of marks instead of a set of formulas they mix up under pressure.
What query it owns: how to understand and revise Methods of Analysing Data in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Methods of Analysing Data revision-guide angle, while Tutopiya’s Methods of Analysing Data subtopic page owns the learning resource and the free Methods of Analysing Data quiz owns the practice.

Methods of Analysing Data is the foundation of the Statistics unit in Cambridge IGCSE Mathematics (0580/0607). Examiners expect you to find the mean, median, mode and range from a list, a frequency table or grouped data — and to choose which average best represents a data set. This guide explains exactly what each measure means, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• The mean is the sum of values divided by how many there are; the median is the middle value when data is ordered; the mode is the most frequent value.
• For grouped data, use mid-interval values to estimate the mean and read the median from a cumulative frequency curve.
• Range measures spread: highest value minus lowest value.
• Always state which average you are calculating and show full working — method marks depend on it.

What are Methods of Analysing Data in Cambridge IGCSE Maths?

Methods of Analysing Data covers the summary statistics used to describe a data set: measures of central tendency (mean, median, mode) and measures of spread (range). In Cambridge IGCSE Mathematics it appears with raw lists, frequency tables, grouped frequency tables and sometimes alongside charts. You must calculate accurately and interpret which average is most appropriate for a given context.

You can read the full explanation, worked examples and notes on Tutopiya’s Methods of Analysing Data subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Measure	What it means	How the exam uses it
Mean	Sum ÷ number of values	”Work out the mean height.”
Median	Middle value (or average of two middles)	“Find the median mass.”
Mode	Most common value	”Write down the modal class.”
Range	Largest − smallest	”Find the range of the scores.”

How to analyse data — step by step

The safest method works for raw lists and extends to frequency tables.

1. Identify the data type — raw list, frequency table or grouped table.
2. For a raw list, order values if finding the median; sum all values for the mean.
3. For a frequency table, multiply each value by its frequency, add, then divide by total frequency for the mean.
4. For grouped data, use the mid-interval of each class: multiply mid-interval by frequency, sum, divide by total frequency.
5. For the median from grouped data, draw or use a cumulative frequency curve and read at n/2.
6. State your answer with units and correct rounding as instructed.

Once you have worked through a few, test yourself with the free Methods of Analysing Data quiz — it tells you fast whether the method has actually stuck.

Raw data vs grouped data: which approach does the question want?

Students lose marks by using the wrong formula or forgetting mid-intervals. Use the table layout to decide.

Situation	What to do	Typical signal words
Short raw list	Direct calculation	”The masses, in kg, are …”
Frequency table	Value × frequency	”The table shows the number of children …”
Grouped table	Mid-interval × frequency	”Class intervals”, “estimate the mean”
Compare averages	State which is better and why	”Which average best represents …”

Methods of Analysing Data in past-paper wording: command words that matter

Most lost marks come from misreading the command word or using the wrong average. These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical stem
Work out / Calculate	Find a numerical average or range	”Work out the mean score.”
Estimate	Grouped data — mid-interval method	”Estimate the mean time.”
Write down	State mode or median without full working	”Write down the modal class.”
Explain which average	Compare mean vs median with reason	”Explain why the median is more suitable.”
Give your answer correct to …	Round as instructed	”Give your answer correct to 2 decimal places.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the formula — is what method marks reward. Here is how three real-style stems are answered.

1. “The marks of 8 students are 45, 52, 52, 60, 63, 70, 72, 80. Work out the mean mark.” Sum = 494. Mean = 494 ÷ 8 = 61.75. Mark-scheme reward: correct sum and division.
2. “The table shows the number of goals scored. Estimate the mean number of goals.” (grouped data) Use mid-intervals × frequencies, divide by total frequency. Reward: clear mid-interval column and Σfx ÷ Σf.
3. “The mean of 5 numbers is 12. Four of the numbers are 8, 10, 14 and 15. Work out the fifth number.” Total = 5 × 12 = 60. Fifth = 60 − (8 + 10 + 14 + 15) = 13. Reward: reverse mean method shown.

When you can recognise the wording instantly, work the full set on the Statistics topical past paper questions and the Methods of Analysing Data quiz to lock the method in.

How Methods of Analysing Data connects to the rest of Statistics

Summary statistics feed directly into Cumulative Frequency, where the median and quartiles are read from a curve. They also underpin Statistical Charts and Diagrams when you interpret bar charts and histograms. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Dividing by the number of classes instead of total frequency in grouped mean questions.
• Forgetting to use mid-intervals for grouped data.
• Confusing modal class (grouped) with mode (single value).
• Finding the median without ordering raw data first.
• Rounding too early and losing accuracy on multi-step reverse-mean questions.

When you need more support

If average and range questions keep tripping you up — especially grouped data — work through the Statistics topical past paper questions and the Methods of Analysing Data quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Methods of Analysing Data hard in Cambridge IGCSE Maths? No — the formulas are straightforward. Marks are lost when students use the wrong average, forget mid-intervals for grouped data, or divide by the wrong total.

What is the quickest way to find the median? Order the data. If there is an odd number of values, the median is the middle one. If even, average the two middle values.

When should I use the median instead of the mean? When the data has extreme values (outliers) that would pull the mean away from the typical value — exam questions often ask you to explain this.

How do I revise Methods of Analysing Data effectively? Read the subtopic notes, practise raw and grouped examples separately, then take the Methods of Analysing Data quiz. Revisit any reverse-mean problems you got wrong before moving on.

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