Find the range of a set of numbers.
The smallest value is subtracted from the largest.
Range: Maximum − Minimum
A range calculator finds the difference between the largest and smallest values in a list. It also reports the minimum and maximum themselves. If a week's afternoon temperatures in Delhi run from 28 °C to 42 °C, the range is 14 °C.
Range is the quickest measure of spread, the first one introduced in school statistics, and often the only one people need for a rough sense of variation. It tells a shop how far its daily sales swing, a teacher how far apart the top and bottom scores are, and a quality inspector how much a batch varies. Its weakness is that it looks only at two numbers, so a single unusual value can make a steady data set look wildly variable.
1. List all the values.
2. Find the largest value, the maximum.
3. Find the smallest value, the minimum.
4. Range = maximum − minimum.
5. Keep the units of the data in the answer, such as °C or ₹.
6. Check for any single value far from the rest that may be inflating the range.
Range uses only the two extremes, so every other value is ignored. Seven temperatures of 30, 31, 31, 32, 32, 33 and 33 °C have a range of 3 °C. Replace the last with a faulty reading of 45 °C and the range jumps to 15 °C, even though six of seven values did not move. This is why range is best used for small, clean data sets or as a first look, and why statisticians prefer measures that use all the data.
The interquartile range, IQR, is the range of the middle half of the data: the third quartile minus the first quartile. By discarding the lowest and highest quarters, it ignores extreme values and describes where most of the data sits. Box plots use the IQR for the box and flag outliers as points more than 1.5 × IQR beyond the box. When a data set has a suspicious extreme, report both the range and the IQR.
Standard deviation measures the typical distance of values from the mean and uses every value, so it is more stable than the range. For data roughly shaped like a bell curve, most values lie within two standard deviations of the mean, so the range of a sample is usually a few standard deviations wide, growing slowly as the sample gets larger. This rough link lets you sanity-check a standard deviation: if it is larger than the range, something is wrong.
Tarun notes the afternoon temperature in Delhi each day for a week in April: 31, 28, 35, 39, 42, 37 and 30 °C.
Answer: Range 14; Minimum 28; Maximum 42
Subtracting the first value from the last in the list instead of the minimum from the maximum.
Reporting the range as 'from 28 to 42' and calling that the range; the range is the single number 14.
Drawing strong conclusions from a range that is driven by one faulty reading.
Comparing ranges of groups with very different sizes; larger samples tend to have larger ranges.
Describing daily or weekly temperature variation.
Showing the gap between the highest and lowest marks in a test.
Quality checks on the spread of weights or sizes in a production batch.
Tracking the swing in daily sales or footfall at a shop.
Quick first look at any data before computing standard deviation.
Is range a good measure of spread?
It is simple, but it only looks at the two most extreme numbers. Variance and standard deviation use every number in the set, so they usually give more useful information.