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Averages are fundamental to data analysis. Students must calculate mean, median, mode and range from raw data, frequency tables and grouped data, and understand which average is most appropriate in different contexts.
Students make these errors again and again. Knowing them in advance gives you a head start.
Forgetting to order the data before finding the median
Dividing by the number of groups instead of the total frequency when finding the mean from a table
Using the class boundaries instead of midpoints for grouped frequency means
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
In probability without replacement, the denominator DECREASES by 1 for each subsequent pick (13 → 12 → 11...). Getting 104/169 instead of the correct answer usually means you forgot this.
“There were very few candidates who did not recognise the significance of the lack of replacement of the first counter, although where this was an issue some still gained credit for an answer of 104/169 with others compounding their error by missing some of the required pairs.”
Source: CIE 0580 · June 2024 · Paper 2 · Q25
For 'exactly one green button' out of two picks, there are TWO orderings: green-then-not OR not-then-green. Calculate one product and DOUBLE it (or add both products).
“Most recognised the need to start off with 5/13 for the probability of a first button being green, which earned a first method mark. Many fewer were able to use this correctly in a product with 8/12 for a second button being non-green to score the next mark. Only the stronger candidates realised that they also needed to double the result of the product to account for the possibility of green being the second button.”
Source: CIE 0580 · November 2023 · Paper 4 · Q15
In a histogram, bar HEIGHT = frequency density (frequency ÷ class width). Find the scale using a bar whose frequency AND width you know, then apply it to the others.
“This proved challenging for many. Those answers displaying understanding that the heights of the blocks of a histogram represented the frequency densities usually had no difficulty. Some clearly showed the calculation of the scale factor for the first bar as 17.2 ÷ 0.86 = 20 and used this correctly with the remaining frequency densities.”
Source: CIE 0580 · June 2022 · Paper 4 · Q5b
Based on 3of 510+ insights extracted from CIE 0580 examiner reports (2018–2024).
This topic is tested by the following exam boards. Our AI tutor covers each one with board-specific content.
Frequency tables organise raw data into categories or class intervals for analysis. Students must construct tables, calculate totals, and use them to find averages and draw statistical diagrams.
Cumulative frequency diagrams show running totals and are used to estimate the median, quartiles and interquartile range. Students draw the characteristic S-shaped curve and read off values at key percentile positions.
Box plots (box-and-whisker diagrams) display the five-number summary of a dataset and are ideal for comparing distributions. Students draw, interpret and compare box plots, calculating the interquartile range and identifying skewness.
GCSE marking is more systematic than most students realise. Understanding M marks, A marks, follow-through rules and QWC can recover marks you did not know you had.
Exam PreparationExaminer reports flag the same errors every sitting. These 10 mistakes cost GCSE maths students marks year after year — and every one of them is fixable with the right habit.
Exam PreparationAfter every GCSE and IGCSE sitting, examiners publish free reports identifying exactly where students lost marks. Almost nobody reads them. Here is how to use them for targeted revision.
Take our free diagnostic quiz to find out exactly where you stand, then practise statistics with our AI tutor.