Grouped Frequency Tables for IGCSE Maths
Estimating the mean and finding the modal class from grouped data. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Un
What You Need to Know
Estimating the mean and finding the modal class from grouped data. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding grouped frequency tables is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Grouped Frequency Tables
Grouped frequency tables organise continuous data into class intervals. Since exact values are unknown, the estimated mean uses the midpoint of each class: mean ≈ Σ(f × midpoint) / Σf. The modal class is the interval with the highest frequency. The median class is found by locating the (Σf/2)th value position. IGCSE 0580 tests estimating the mean, identifying the modal class, and determining the median class interval.
Step-by-Step Method
- 1
Find class midpoints
Add the class boundaries and divide by 2: for interval 20 ≤ x < 30, midpoint = 25.
- 2
Calculate f × midpoint for each class
Multiply each frequency by its midpoint. Sum all these products.
- 3
Estimated mean = Σ(f × mid) / Σf
Divide the total of f×mid by the total frequency.
- 4
Modal class
The class with the highest frequency — state it as an interval, not a single value.
- 5
Median class
Find the Σf/2 th position. Cumulate frequencies to find which class contains this position.
Worked Example
Question
Heights (cm): 150–<160 (f=5), 160–<170 (f=12), 170–<180 (f=9), 180–<190 (f=4). Estimate the mean and state the modal class.
Solution
Midpoints: 155, 165, 175, 185. f×mid: 5×155=775, 12×165=1980, 9×175=1575, 4×185=740. Σ(f×mid) = 775+1980+1575+740 = 5070 Σf = 5+12+9+4 = 30 Estimated mean = 5070/30 = 169 cm Modal class = 160–<170 (highest frequency 12) Answers: Mean ≈ 169 cm; Modal class: 160–<170
Exam Tips for Grouped Frequency Tables
- Use the midpoint of each class — never the lower or upper bound.
- Modal class is the interval with highest frequency — it is NOT a single value.
- The estimated mean is an approximation — state it clearly as 'estimated mean'.
- Σ(f × midpoint) should be in the thousands for large data sets — a small result indicates an arithmetic error.
Practice Questions
Q1: Ages: 0–<10 (f=8), 10–<20 (f=15), 20–<30 (f=12), 30–<40 (f=5). Estimate the mean age.
Show hint
Midpoints: 5,15,25,35. Σ(f×mid)=40+225+300+175=740. Σf=40. Mean=740/40=18.5.
Q2: For the table above, which class contains the median?
Show hint
Σf=40. Median at 20th position. Cumulate: 8, 23. 20th is in 10–<20.
Q3: A student estimates mean from grouped data as exactly 24.0. What assumption was made?
Show hint
The midpoint of each class was used as a representative value — all data within a class cluster exactly at the midpoint.
Frequently Asked Questions
What is grouped frequency tables in IGCSE Maths?
Estimating the mean and finding the modal class from grouped data.
Is grouped frequency tables in the Core or Extended syllabus?
Grouped Frequency Tables is part of the Core and Extended syllabus for IGCSE Mathematics 0580.
How do I revise grouped frequency tables 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 grouped frequency tables rather than trying to cover everything at once.
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