Cumulative Frequency for IGCSE Maths
Drawing cumulative frequency curves and finding median, quartiles, and IQR. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Und
What You Need to Know
Drawing cumulative frequency curves and finding median, quartiles, and IQR. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding cumulative frequency is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Cumulative Frequency
A cumulative frequency table/graph shows the total frequency up to each class boundary. The cumulative frequency curve (ogive) is used to find the median (at the 50th percentile), lower quartile Q₁ (25th percentile), upper quartile Q₃ (75th percentile), interquartile range IQR = Q₃ − Q₁, and percentiles. IGCSE Extended Paper 4 regularly asks for these statistics from a given ogive, and sometimes asks students to draw the curve.
Step-by-Step Method
- 1
Build the cumulative frequency table
Add up frequencies progressively. Each cumulative frequency entry is the total of all frequencies up to that point.
- 2
Plot the ogive
Plot (upper class boundary, cumulative frequency) for each class. Start from (lower boundary of first class, 0). Join with a smooth curve.
- 3
Read the median
Median is at cumulative frequency = n/2. Draw a horizontal line at n/2, find where it hits the curve, drop to the x-axis.
- 4
Find quartiles
Q₁ at n/4; Q₃ at 3n/4. Same process as median.
- 5
IQR and percentiles
IQR = Q₃ − Q₁. For the kth percentile: use cumulative frequency = kn/100.
Worked Example
Question
80 students took a test. From the ogive: Q₁ = 45, median = 60, Q₃ = 72. Find: (a) IQR (b) number of students scoring more than 70.
Solution
Part (a): IQR = Q₃ − Q₁ = 72 − 45 = 27 Part (b): Read cumulative frequency at score = 70 from the ogive. Suppose the ogive reads CF = 62 at score = 70. Number scoring ≤ 70 = 62. Number scoring > 70 = 80 − 62 = 18. Answers: (a) IQR = 27 (b) 18 students
Exam Tips for Cumulative Frequency
- Plot points at the UPPER class boundary, not the midpoint.
- Always draw a smooth curve — not straight lines between points. The ogive is always concave then convex.
- Median at n/2 (not (n+1)/2 — because it is a continuous graph).
- For 'number of students above x': read CF at x, then subtract from n.
Practice Questions
Q1: A cumulative frequency graph has n=100. Estimate the median, Q1, and Q3 by reading at the 50th, 25th, and 75th cumulative frequencies.
Show hint
Read the x-values where the CF curve passes through y=50 (median), y=25 (Q1), and y=75 (Q3).
Q2: From an ogive, Q₁=28 and Q₃=52. Find the IQR and comment on the spread.
Show hint
IQR=52−28=24. This means the middle 50% of data spans a range of 24 units.
Q3: Why is IQR preferred over Range as a measure of spread for skewed distributions?
Show hint
IQR ignores the extreme 25% at each end, making it resistant to outliers. Range is affected by every data point.
Frequently Asked Questions
What is cumulative frequency in IGCSE Maths?
Drawing cumulative frequency curves and finding median, quartiles, and IQR.
Is cumulative frequency in the Core or Extended syllabus?
Cumulative Frequency is part of the Extended only syllabus for IGCSE Mathematics 0580.
How do I revise cumulative frequency effectively?
Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on cumulative frequency rather than trying to cover everything at once.
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