Range Calculator
Enter comma-separated numbers to find the statistical range, minimum, maximum, midrange, and IQR instantly — with a complete summary of your data's spread and boundaries.
Enter your values above to see the results.
Tips & Notes
- ✓Never use range as your only spread measure. It ignores all values between the minimum and maximum. A single outlier can make range misleadingly large while the rest of the data is tightly clustered.
- ✓IQR is almost always more informative than range for real-world data. IQR covers the middle 50% of values and is completely unaffected by extreme outliers.
- ✓Range = 0 means all values are identical — zero variability. Any non-zero range means at least some variation exists, but a large range alone does not tell you where most values fall.
- ✓For quality control applications, range charts (R-charts) track sample range over time to detect process instability. They work well for small samples (n=2 to 10) where standard deviation estimates are unreliable.
- ✓Midrange is not the same as median. Midrange=(max+min)/2 is pulled by extremes just like the mean. Median is the actual middle value after sorting and is far more robust for asymmetric data.
Common Mistakes
- ✗Using range as the primary description of data spread. Data [1,50,50,50,50,51] and [1,25,50,75,100] both have range=50, but their distributions are completely different. Range hides this entirely.
- ✗Confusing midrange with median. Midrange=(max+min)/2 for [1,2,3,4,100] = 50.5. Median = 3. These are vastly different — midrange is distorted by the outlier; median is not.
- ✗Treating a large range as evidence of outliers. A large range only shows that two extreme values exist — it does not tell you whether most data is concentrated in one area or spread uniformly. Always check with a histogram or IQR.
- ✗Computing range from an unsorted list by taking last minus first. Always find the actual minimum and maximum values, regardless of order in the data entry.
- ✗Forgetting that range has the same units as the data. If data is in centimeters, range is in centimeters. Range is not a dimensionless ratio — do not compare ranges across datasets with different units.
Range Calculator Overview
The range is the simplest measure of spread in a dataset: the distance from the lowest value to the highest. It answers the most basic spread question — how wide is the data? A weekly temperature range of 15°C tells you conditions varied significantly. A range of 2°C tells you the week was remarkably stable. Despite its simplicity, range has a critical weakness: it is completely determined by just two values and ignores everything in between.
Range — distance from minimum to maximum:
Range = Maximum − Minimum
EX: Weekly temperatures [18, 21, 24, 19, 23, 27, 22] → Min=18, Max=27 → Range = 27−18 = 9°CMidrange — center of the data's spread:
Midrange = (Maximum + Minimum) / 2
EX: Min=18, Max=27 → Midrange = (18+27)/2 = 22.5°C — the midpoint between the extremesInterquartile range (IQR) — outlier-resistant spread:
IQR = Q3 − Q1
EX: Data [18,19,21,22,23,24,27] → Q1=19, Q3=24 → IQR = 24−19 = 5°C (vs. Range = 9°C)Comparing spread measures — when to use each:
| Measure | Formula | Uses How Many Points | Outlier Sensitive? | Best For |
|---|---|---|---|---|
| Range | Max − Min | 2 (only extremes) | Extremely | Quick preliminary check |
| IQR | Q3 − Q1 | Middle 50% | Not at all | Skewed data, outlier detection |
| Standard Deviation | √[Σ(x−x̄)²/(n−1)] | All values | Yes — moderately | Normal data, hypothesis testing |
| Variance | SD² | All values | Yes — moderately | Statistical formulas and calculations |
Frequently Asked Questions
The range is the difference between the maximum and minimum values in a dataset: Range = Max − Min. Example: test scores [55, 62, 70, 78, 85, 90, 95] → Range = 95 − 55 = 40. The range tells you the total spread of your data from lowest to highest. It is the simplest spread measure but is sensitive to outliers and ignores everything between the extremes.
Range = Max − Min uses only the two extreme values. IQR = Q3 − Q1 uses the 25th and 75th percentiles — the spread of the middle 50%. Example: [1, 2, 3, 4, 5, 6, 100]: Range = 99 (dominated by the outlier 100), IQR = 4 (unaffected by 100, measuring only the central data). IQR is almost always more informative for real-world data that contains outliers.
Range uses only two values — the minimum and maximum — regardless of dataset size. It ignores all values in between. One outlier can change it dramatically: [10, 11, 12, 13, 14] has range=4. Add one outlier to get [10, 11, 12, 13, 14, 200] and range=190. The 5 original tightly-clustered values have not changed, but range increases 47-fold. Standard deviation and IQR account for all values and are far more reliable.
Midrange = (Maximum + Minimum) / 2. It is the midpoint of the extremes, not the center of the actual data. Median is the middle value when data is sorted. For [1,2,3,4,100]: Midrange = (1+100)/2 = 50.5, Median = 3. The outlier 100 pulls midrange to 50.5 — far from where most values sit. Median is unaffected. Midrange is rarely used in professional statistics; median is almost always preferred.
Yes. Range = 0 when all values in the dataset are identical. Example: [7, 7, 7, 7, 7] → Range = 7 − 7 = 0. This means there is zero variability — every observation is the same. In practice, range = 0 in a real-world dataset often indicates a measurement error, data entry problem, or a sensor that is not functioning correctly.
Range is useful for quick preliminary data checks, simple communication to non-technical audiences, and quality control (R-charts for small samples). 'Temperatures ranged from 15°C to 38°C this summer' is immediately understood. However, for any serious statistical analysis, supplement range with IQR (robust spread) and standard deviation (accounts for all values). Range alone never tells the complete story.