The mean, mode, and median are the three ways we describe the 'centre' of a set of data. Each tells a slightly different story about the data, and WAEC tests all three: sometimes in the same question.
Mean
Mean = Sum of all values ÷ Number of values From a frequency table: Mean = Σ(fx) ÷ Σf, where f is frequency and x is the value. Example: Data: 4, 7, 7, 9, 13 Mean = (4 + 7 + 7 + 9 + 13) / 5 = 40 / 5 = 8
Median
The median is the middle value when data is arranged in order. • Odd number of values: median is the middle one. • Even number: median is the average of the two middle values. Example: 3, 5, 7, 9, 11 → Median = 7 (3rd value) Example: 3, 5, 7, 9 → Median = (5 + 7) / 2 = 6
Mode
The mode is the value that appears most often. A data set can have: • One mode (unimodal) • Two modes (bimodal) • No mode (all values appear once) Example: 2, 3, 3, 4, 5, 5, 5, 7 → Mode = 5
Key points
- Mean = Σx / n, or Σfx / Σf from a frequency table
- Median: sort the data first, then find the middle
- Mode: the value with the highest frequency
- WAEC often asks which measure best represents the data
- The mean is affected by extreme values; median is more resistant
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WAEC tip
When a WAEC question gives a frequency table, always add an 'fx' column. It's the fastest way to calculate the mean and median class with no errors.
Practise this
Find the mean, median, and mode of: 6, 8, 8, 10, 12, 14, 8, 6, 10, 8. Then state which measure best represents this data and why.
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