Range Calculator — Find the Spread of Any Data Set
Find the range of any data set with step-by-step explanation. For standard deviation, try our standard deviation calculator.
Table of Contents
Find the Range
Enter your data values as comma-separated numbers.
Range – Complete Explanation
The range is the simplest measure of dispersion — the distance between the smallest and largest values.
Range Formula
Range = Maximum - Minimum
1. What Is the Range?
It answers: "How far apart are the extremes in my data?"
- Simple: Just two values needed.
- Same units as data.
- Sensitive to outliers.
2. How to Find the Range
- Sort data.
- Identify min (first) and max (last).
- Subtract: Range = Max - Min.
3. Step-by-Step Examples
3.1 Example 1: Basic
12, 5, 23, 8, 17, 9, 14 Sorted: 5, 8, 9, 12, 14, 17, 23 Min = 5, Max = 23 Range = 23 - 5 = 18
3.2 Example 2: Negative Values
-8, 3, -2, 15, 0, -5, 11 Min = -8, Max = 15 Range = 15 - (-8) = 23
4. More Examples
75, 82, 90, 68, 95, 88 → Range = 27
72, 75, 71, 74, 73 → Range = 4
Single value: 42 → Range = 0
5. Range vs. Other Measures of Dispersion
Range: Max - Min. Uses 2 points. Outlier-sensitive.
IQR: Q₃ - Q₁. Middle 50%. Robust.
Standard Deviation: Every data point. Moderate outlier sensitivity.
6. Interquartile Range (IQR)
IQR Formula
IQR = Q₃ - Q₁
7. Limitations of the Range
- Outlier sensitivity — one extreme value inflates the range.
- Ignores distribution shape — two data sets with same range can look very different.
- Grows with sample size — hard to compare ranges from different-sized samples.
8. Common Mistakes to Avoid
- Forgetting to sort
- Subtracting in wrong order — always Max - Min.
- Confusing range with mid-range — mid-range = (Max+Min)/2 is a center, not spread.
9. Real-World Applications
- Weather: Daily temperature range.
- Stock Market: Daily price range (volatility).
- Quality Control: Measurement range monitoring.
- Education: Test score gap between highest and lowest.
10. Practice Problems with Solutions
15, 22, 8, 19, 31, 14 → Range = 23
-5, 0, 12, -3, 8, -1 → Range = 17
Range = 50, Min = 20 → Max = 70
Class A: 65-98 vs Class B: 72-88 → A has more variability
11. Tips for Mastering the Range
- Always sort first.
- Pair range with IQR and standard deviation for complete picture.
- Report min and max alongside range.
12. Final Thoughts
The range is statistics at its most intuitive. Use this calculator to verify your work, but practice manually to build statistical intuition.
13. Frequently Asked Questions
Yes. By definition, the maximum is greater than or equal to the minimum, so Range = Max - Min is always ≥ 0. A zero range means all values are identical. If you get a negative range, you've subtracted in the wrong order.
The range uses all data from min to max, making it sensitive to outliers. The interquartile range (IQR) uses only the middle 50% of data (Q₃ - Q₁), ignoring the extremes. IQR is more robust and preferred when outliers are present.
No. The range requires numerical data because it involves subtraction. For categorical data, use the mode (most frequent category) instead. For ordinal data (ordered categories), you can describe the spread but not calculate a numerical range.
The range has the same units as the original data. If you measure heights in inches, the range is in inches. If you measure temperatures in Celsius, the range is in Celsius. This makes it easy to interpret — unlike variance (squared units) or standard deviation (also original units).
The mid-range is the average of the maximum and minimum: (Max + Min)/2. It's a measure of central tendency, not dispersion. Unlike the range which measures spread, the mid-range estimates the center of the data. It's rarely used in practice because it's highly sensitive to outliers.
Explore Math Topics
Continue your learning journey with our other math guides
Conclusion
The range is statistics at its most intuitive. Use this calculator to verify your work, but practice manually to build statistical intuition and pair it with other measures of dispersion.
Readers who wish to continue practicing and reinforce what they've learned can explore the companion learning resource for guided exercises.