The range is the simplest measure of spread: the distance from the smallest value to the largest. It answers questions like “how far apart were the high and low temperatures this week?” or “what is the gap between the cheapest and most expensive quote?” This calculator finds the range together with the minimum, maximum and midrange, and adds the interquartile range so you can see how much of the spread comes from the extremes.
How to use the range calculator
- Type or paste your numbers, separated by commas, spaces or line breaks.
- Read the range on the tape, along with the minimum, maximum, midrange, interquartile range and count.
- Open Show the work to see the sorted data and each subtraction.
Range formulas
The calculator finds quartiles with the median-of-halves method used on TI-84 calculators.
Worked example
A week of daily high temperatures in °F: 68, 74, 71, 79, 83, 77, 70.
- Sort: 68, 70, 71, 74, 77, 79, 83.
- Minimum and maximum: 68 and 83.
- Range: 83 − 68 = 15 °F.
- Midrange: (68 + 83) ÷ 2 = 75.5 °F.
- IQR: the lower half 68, 70, 71 has median 70 and the upper half 77, 79, 83 has median 79, so the IQR is 79 − 70 = 9 °F.
So the week swung through 15 degrees, but the middle half of the days stayed within a 9-degree band.
Range in context
Where the range is useful
- Quick quality checks. Manufacturing control charts often track the range of small samples (for example, five parts measured each hour), because it is fast to compute and, for small samples, nearly as informative as the standard deviation.
- Weather and markets. Daily temperature ranges and a stock’s 52-week high–low range are reported as ranges because people care about the extremes themselves.
- Rough estimates of spread. For bell-shaped data, a sample of about 30 to 100 values typically spans 4 to 5 standard deviations, so range ÷ 4 is a quick back-of-the-envelope standard deviation.
Where it misleads
Because it depends on only two numbers, the range reacts strongly to a single outlier. Add one 98-degree heat-wave day to the example above and the range jumps from 15 to 30, while the IQR barely moves. The range also tends to grow with sample size: the more values you collect, the more likely you are to catch an extreme one. Compare ranges only between samples of similar size.
| Measure | Uses | Sensitive to outliers? |
|---|---|---|
| Range | 2 values | Very |
| Interquartile range | middle 50% | No |
| Standard deviation | every value | Somewhat |
For a robust picture of spread use the quartile calculator or the five number summary calculator; for the most common formal measure use the standard deviation calculator.
Frequently asked questions
How do you find the range of a data set?
Subtract the smallest value from the largest. For 68, 74, 71, 79, 83, 77 and 70, the range is 83 − 68 = 15.
Can the range be negative?
No. The maximum is always at least as large as the minimum, so the range is zero or positive. It is zero only when every value is the same.
What is the midrange?
The midrange is the average of the minimum and maximum, (min + max) ÷ 2. It is a quick measure of center, but because it depends on only the two most extreme values it is easily distorted by an outlier.
Why is the range a weak measure of spread?
It uses only two values, so one unusual observation can change it dramatically, and it tends to grow as you collect more data. The interquartile range and standard deviation use more of the data and are more stable.