Two cities both average 20°C a year. One swings 0–40°C; the other stays 18–22°C. Same mean, wildly different lives. The range is the first hint of how spread out data is.
The range is the difference between the largest and smallest values: max − min. It's the simplest measure of spread.
Quality control tolerances, temperature swings, salary bands, test-score spread — the range is the quick-and-dirty 'how variable is this?' number.
Test scores: 55, 88, 72, 91, 60, 88. What's the range?
Compare spread: Set A = {19, 20, 21}, Set B = {0, 20, 40}.
Both have mean 20. Range of A = 2, range of B = 40. Set B is far more spread out — the mean alone wouldn't tell you that.
The range only uses two values — the extremes. One weird outlier blows it up entirely. For a robust spread measure, use the interquartile range (IQR) or standard deviation.
Range is the appetiser; standard deviation is the main course. Use range for a quick gut-check, SD when you need a real spread measure.
- Range = max − min.
- Simplest spread measure — but uses only the two extremes.
- Fragile to outliers; prefer IQR or SD for serious work.