Edexcel IGCSE Maths (4MA1) · Unit 6: Statistics & Probability
IGCSE Maths Mean, Median and Mode Questions and Answers
Mean, Median and Mode questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 4 worked examples first, then cover each solution and redo it yourself.
Averages & basic data handling: Calculating mean, median, mode and range from a data set.
Statistical Measures 1: Mean, median, mode from a list of values.
Statistical Measures 2: Mean from a frequency table (grouped or ungrouped).
Statistical Measures 3: Range and IQR — measures of spread.
Mean, Median and Mode worked examples
Worked example 1: Mean and median
Find the mean and the median of 3, 8, 8, 10, 11.
Solution
Mean: \((3+8+8+10+11)\div5=40\div5=8\).
The list is already in order; the middle (3rd) value is 8.
Answer: Mean 8, median 8
Tip: Always order the data before finding the median.
Worked example 2: Averages from a list
Find the mean, median and mode of 4, 9, 6, 12, 9.
Solution
Mean \(=40\div5=8\).
Ordered: 4, 6, 9, 9, 12, so median 9.
Mode 9.
Answer: Mean 8, median 9, mode 9
Tip: Order the list first.
Worked example 3: Mean from a frequency table
Values 1, 2, 3, 4 have frequencies 3, 5, 8, 4. Find the mean.
Solution
\(\Sigma fx=3+10+24+16=53\).
\(\Sigma f=20\).
Mean \(=53\div20=2.65\).
Answer: 2.65
Tip: Divide by the total frequency, not the number of rows.
Worked example 4: Estimated mean
Estimate the mean for: \(0<x\le10\): 5; \(10<x\le20\): 8; \(20<x\le30\): 7.
Solution
Midpoints 5, 15, 25.
\(\Sigma fx=25+120+175=320\).
Mean \(\approx320\div20=16\).
Answer: 16
Tip: It is an estimate because midpoints are used.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Which Edexcel IGCSE Maths papers test mean, median and mode?
Either Higher tier paper, 1H or 2H, can test mean, median and mode: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more mean, median and mode questions?
In the IGCSE student hub: Unit 6 (Statistics & Probability) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
IGCSE Math Revision