Cumulative Frequency
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.
What You'll Learn
- Constructing a cumulative frequency table
- Drawing a cumulative frequency graph (S-curve)
- Estimating the median and quartiles from the graph
- Calculating the interquartile range
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Plotting cumulative frequency at the midpoint instead of the upper class boundary
Joining points with straight lines instead of a smooth curve
Reading the median from the wrong axis on the graph
What Examiners Say About Cumulative Frequency
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Common Mistake●●●●●
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.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q25
- Common Mistake●●●●●
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).
Source: CIE 0580 · May/June 2023 · Paper 4 · Q15
- Technique●●●●●
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.
Source: CIE 0580 · Feb/March 2022 · Paper 4 · Q5b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Box Plots
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.
Frequency Tables
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.
Histograms
Histograms display continuous grouped data using bars whose area (not height) represents frequency. This topic requires students to calculate frequency density and interpret histograms with unequal class widths.
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Worked examples and data interpretation guides