Range - How Spread Out Is Your Data?
The range measures how spread out a dataset is. It is the simplest measure of spread and is calculated by subtracting the smallest value from the largest value. A large range means the data is spread widely; a small range means the data is clustered together.
The Formula
Range = Largest value − Smallest value
The range tells you the width of the dataset – how much the values vary from one extreme to the other.
Worked Examples
Largest = 21, Smallest = 3. Range = 21 − 3 = 18.
Class A: Range = 80 − 45 = 35. Class B: Range = 68 − 61 = 7.
Class B scores are far more consistent; Class A is much more spread out.
Largest = 18 C, Smallest = 7 C. Range = 18 − 7 = 11 C.
Limitation of the Range
The range only uses two values – the maximum and minimum. One extreme outlier can make the range very large, even if most of the data is tightly clustered. For example: {5, 6, 6, 7, 7, 7, 100} has range 95, yet six of the seven values are between 5 and 7.
Range in Context
| Small range | Large range |
|---|---|
| Data is consistent / reliable | Data is variable / spread out |
| Example: a runner's consistent race times | Example: unpredictable weather temperatures |
Key Takeaways
- Range = Largest − Smallest. It measures the spread of data.
- A small range = consistent data. A large range = variable data.
- The range is simple to calculate but sensitive to outliers.
- Use the range alongside averages (mean, median, mode) for a fuller picture.
Practice Questions
- Find the range of: 23, 11, 47, 5, 38, 19.
- Team A goals per match: 1, 3, 2, 4, 1, 2, 5, 3. Team B: 2, 2, 3, 2, 2, 3, 2, 2. Compare the ranges and comment on consistency.
- Temperatures in July: 28, 31, 25, 33, 29, 27, 35, 30, 26, 32 (Celsius). Find the range.
- A dataset has a range of 20. The smallest value is 13. What is the largest value?
- Five values are 7, 10, ?, 15, 20 (in order). The range is 16. Find the missing value if it is not the maximum or minimum.