📊 Mean, median and mode
Big Idea: Measures of central tendency find the 'middle' or 'typical' value in a data set. The three main measures are mean, median and mode. 🎯
Mean (average)
- Add up all values ÷ number of values
- Uses every data point — most common measure
- Can be distorted by extreme values (outliers)
Median (middle value)
- Put values in order, find the middle one
- Not affected by outliers
- Good for skewed data (e.g. salary data)
Mode (most common value)
- The value that appears most often
- Can have no mode, one mode, or multiple modes
- Useful for categorical data (e.g. most popular product)
🤔 When to use each
- Mean — best for evenly spread data with no extreme outliers
- Median — best when outliers could distort the average (e.g. wages, house prices)
- Mode — best for finding the most popular item (e.g. best-selling shoe size)
Mean = add and divide. Median = middle of ordered list. Mode = most frequent. Easy! 🧮
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📝 Worked examples
Data set: 5, 8, 8, 10, 12, 15, 50
- Mean = (5+8+8+10+12+15+50) ÷ 7 = 108 ÷ 7 = 15.4
- Median = 10 (the 4th value when ordered — middle of 7 values)
- Mode = 8 (appears twice, more than any other value)
- Note: the mean (15.4) is pulled up by the outlier (50). The median (10) is more representative here.
Exam tip: If a question gives you data with an obvious outlier, comment on how the mean is distorted and suggest the median as a better measure.