Range
Difference between the largest and smallest values.
Formula
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Example
Data 3..17: R=14
How it works
The range tells you how spread out a set of numbers is by comparing the two extreme values. It works because the largest value sets the top end of the data and the smallest value sets the bottom end, so subtracting them gives the total span covered. A bigger range means the data are more spread out; a smaller range means they are more tightly clustered.
When to use it
Use the range when you want a quick measure of variability, especially for small data sets or simple comparisons. It is common in basic statistics, science experiments, weather data, and sports scores when you only need the overall spread.
Worked example, step by step
Data values: 5, 8, 12, 19, 23 Step 1: Identify the maximum value: x_max = 23 Step 2: Identify the minimum value: x_min = 5 Step 3: Subtract: R = x_max - x_min Step 4: R = 23 - 5 = 18 Final answer: The range is 18.
Common mistakes to avoid
- Subtracting the smallest value from the largest the wrong way around and getting a negative answer
- Using two middle values instead of the maximum and minimum
- Thinking the range shows how many numbers are in the data set rather than how far apart the extremes are
Did You Know?
The range is the simplest measure of spread but also the most fragile — a single outlier can distort it completely.
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More in Statistics & Probability
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BasicThe average of a data set.
Median
BasicThe middle value separating the higher and lower halves.
Variance
IntermediateAverage squared deviation from the mean.
Standard Deviation
IntermediateSquare root of the variance; typical spread.
Z-Score
IntermediateNumber of standard deviations a value is from the mean.
Bayes' Theorem
IntermediateUpdates a probability given new evidence.