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Core + Extended Statistics

Mean, Median, Mode, Range for IGCSE Maths

Calculating and comparing measures of average and spread. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understandi

What You Need to Know

Calculating and comparing measures of average and spread. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding mean, median, mode, range is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Mean, Median, Mode, Range

The three measures of average (mean, median, mode) and the range are tested in all IGCSE 0580 papers. Mean = sum of all values / number of values. Median = middle value when ordered (or average of two middle values for an even count). Mode = most frequent value. Range = largest − smallest. For frequency tables: mean = Σ(f×x)/Σf. The choice of appropriate average depends on the data: median is better for skewed data; mean uses all values.

Step-by-Step Method

  1. 1

    Find the mean

    Add all values and divide by the count. For a frequency table: mean = Σ(f × x) / Σf.

  2. 2

    Find the median

    Order the data. Position = (n+1)/2. For even n, average the two middle values.

  3. 3

    Find the mode

    The value that appears most often. There can be no mode, one mode, or multiple modes.

  4. 4

    Find the range

    Range = maximum value − minimum value.

  5. 5

    Interpret and choose

    Use median when there are extreme outliers. Use mean when all data points matter equally. Mode for categorical or discrete data with a clear most-common value.

Worked Example

Question

Data: 3, 7, 4, 7, 5, 9, 7, 2, 6. Find the mean, median, mode, and range.

Solution

Sorted: 2, 3, 4, 5, 6, 7, 7, 7, 9 Mean = (2+3+4+5+6+7+7+7+9)/9 = 50/9 = 5.56 (3 s.f.) Median: 9 values. Middle is 5th value = 6. Mode = 7 (appears 3 times). Range = 9 − 2 = 7. Answers: Mean ≈ 5.56; Median = 6; Mode = 7; Range = 7

Exam Tips for Mean, Median, Mode, Range

  • Always sort data before finding the median — unsorted data gives wrong median positions.
  • For frequency tables: multiply each value by its frequency FIRST, then sum and divide by total frequency.
  • The median position is (n+1)/2, NOT n/2 — for 9 data points, median is in position 5 (not 4.5).
  • Range is NOT a measure of average — it measures spread.

Practice Questions

Q1: Frequency table: x=1 (f=3), x=2 (f=5), x=3 (f=4), x=4 (f=2), x=5 (f=1). Find the mean.

Show hint

Σ(fx)=3+10+12+8+5=38. Σf=15. Mean=38/15=2.53.

Q2: The mean of 6, 8, x, 12, 14 is 10. Find x.

Show hint

Sum = 10×5=50. 6+8+x+12+14=50 → x=10.

Q3: Which average is most appropriate for a data set with one very large outlier? Justify.

Show hint

Median — it is not affected by extreme values, while the mean would be pulled toward the outlier.

Frequently Asked Questions

What is mean, median, mode, range in IGCSE Maths?

Calculating and comparing measures of average and spread.

Is mean, median, mode, range in the Core or Extended syllabus?

Mean, Median, Mode, Range is part of the Core and Extended syllabus for IGCSE Mathematics 0580.

How do I revise mean, median, mode, range 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 mean, median, mode, range rather than trying to cover everything at once.

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