An SAT Math micro-topic under Center, spread, and shape of distributions (Problem solving and data analysis). Free to read — no account needed.
The range measures spread: it is the largest value minus the smallest value. First find the highest and lowest numbers, then subtract. The bigger the gap between them, the bigger the range.
For 20,14,32,48,23,35,40, the highest is 48 and the lowest is 14. So the range is 48−14=34. You only need those two extreme values.
When two sets are combined, use the overall highest and lowest. If one set runs from 16 to 81 and another from 22 to 88, the combined range uses 16 and 88. So the range is 88−16=72.
The range depends only on the two extreme values, not on anything in between. Changing a middle number does not change the range. Only the largest and smallest values matter.
Worked examples
What is the range of 1,4,6,9? The largest is 9 and the smallest is 1. So the range is 9−1=8.
What is the range of 12,7,20,3,15? The largest is 20 and the smallest is 3. So the range is 20−3=17.
Set A runs from 10 to 45, and set B runs from 20 to 60. What is the range when the two sets are combined? The overall largest is 60 and the smallest is 10. So the range is 60−10=50.
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