Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want methods of analysing data — mean, median, mode, range and grouped-data estimates — 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 sit at the heart of the Statistics unit in Cambridge IGCSE Mathematics (0580/0607). Examiners expect you to choose the correct average, calculate from raw or grouped tables, and interpret what each measure tells you about a data set. This guide explains the core methods, the question types that actually appear, and where to practise each skill.

Key takeaways

• Mean uses all values; median is the middle value; mode is the most frequent; range measures spread.
• For grouped data, use mid-interval values and Σfx for an estimated mean.
• The exam often asks you to compare two data sets using averages and range — state which is higher and what that means.
• Always show full working for mean and median; method marks depend on it.

What are methods of analysing data in Cambridge IGCSE Maths?

Methods of analysing data are the statistical tools used to summarise a set of numbers: calculating averages (mean, median, mode), measuring spread (range), and estimating values from grouped frequency tables. In Cambridge IGCSE Mathematics they appear in short calculation questions and in longer interpretation stems where you must explain which average best represents the data.

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.

Idea	What it means	How the exam uses it
Mean	Sum of values ÷ number of values	”Work out the mean height.”
Median	Middle value when ordered	”Find the median age.”
Mode	Most common value	”Write down the modal class.”
Grouped mean	Σfx ÷ Σf using mid-intervals	”Estimate the mean from the table.”

How to analyse data — step by step

The safest method works for raw lists and frequency tables alike.

1. Identify what is asked — mean, median, mode or range.
2. For raw data, order values if finding the median; count frequencies for the mode.
3. For a frequency table, multiply each value by its frequency for Σfx.
4. For grouped data, use the mid-interval of each class as x.
5. Calculate mean = Σfx ÷ Σf; median from the cumulative position n/2.
6. Interpret — compare averages and comment on spread using range.

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 in grouped tables.

Situation	What to do	Typical signal words
Short list of values	Add and divide for mean; order for median	”The marks were 4, 7, 7, 9, 12”
Ungrouped frequency table	Use each value × frequency	”Number of goals scored” with a tally
Grouped frequency table	Mid-interval × frequency	”Estimate the mean mass” from a class table
Compare two groups	Calculate both means/medians and range	”Which class did better on average?”

Methods of analysing data in past-paper wording: command words that matter

Most lost marks come from misreading the command word or using mean when median is more appropriate.

Command word / phrase	What the question wants	Typical stem
Work out / Calculate	Full method for an average or range	”Work out the mean of the 12 values.”
Estimate	Grouped-data mean using mid-intervals	”Estimate the mean time, giving your answer correct to 1 decimal place.”
Write down	Mode or median from a simple table	”Write down the modal score.”
Compare	Two averages and a comment	”Compare the results of Group A and Group B.”
Explain which average	Justify mean vs median	”Explain why the median is a better average for this data.”

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 masses of 8 apples (in grams) are 120, 125, 130, 130, 135, 140, 145, 150. Work out the mean mass.” Sum = 1075; mean = 1075 ÷ 8 = 134.4 g (1 d.p.). Mark-scheme reward: correct sum and division shown.
2. “Estimate the mean height from the grouped frequency table.” Use mid-intervals, calculate Σfx and Σf, then mean = Σfx ÷ Σf. Reward: mid-interval column shown before the final answer.
3. “Group A has mean 72 and range 40. Group B has mean 68 and range 12. Compare the two groups.” A has a higher average but more spread; B is more consistent. Reward: references both mean and range in the comparison.

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 connect to the rest of Statistics

Averages and range 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 Σf in grouped mean questions.
• Forgetting to order data before finding the median.
• Calling the highest class the mode instead of the class with greatest frequency.
• Using the upper class boundary instead of the mid-interval for grouped estimates.
• Comparing groups using mean only when the question asks for spread as well.

When you need more support

If average and range questions keep tripping you up — especially grouped-data estimates — 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 grouped-data mean hard in Cambridge IGCSE Maths? No — the method is always Σfx ÷ Σf using mid-intervals. Marks are lost when students skip the mid-interval column or divide by the wrong total.

When should I use the median instead of the mean? Use the median when the data has extreme values or is skewed — exam questions often hint at this with “one very high value” or ask you to explain your choice.

What is the difference between modal class and mode? For grouped data the mode is the modal class (the class with highest frequency), not a single exact value.

How do I revise methods of analysing data effectively? Read the subtopic notes, practise both raw and grouped tables, then take the Methods of Analysing Data quiz. Revisit any comparison questions you could not explain in words.

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