Range
The difference between the largest and smallest values.
Formula
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Example
Range of {4,9,2} = 7
How it works
The range measures how spread out a set of values is by comparing the highest value to the lowest value. Subtracting the minimum from the maximum gives the total distance covered by the data, so a larger range means the values are more widely separated. It is a quick way to describe variation, though it does not show what happens between the extremes.
When to use it
Use the range when you want a fast, simple measure of spread in a list of numbers, such as test scores, temperatures, or experimental results. It is especially useful for comparing how variable two small data sets are.
Worked example, step by step
Data set: {12, 7, 19, 15} Step 1: Identify the maximum value, x_max = 19 Step 2: Identify the minimum value, x_min = 7 Step 3: Substitute into the formula: R = x_max - x_min Step 4: Calculate: R = 19 - 7 = 12 Final answer: The range is 12
Common mistakes to avoid
- adding all the values instead of subtracting the minimum from the maximum
- using the middle numbers rather than the largest and smallest values
- forgetting to sort the data or check carefully which value is greatest and which is least
Did You Know?
The range is the simplest measure of spread, but a single outlier can blow it wide open.
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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.