Range (Statistics)
In short: Range in statistics is the distance from the smallest to the largest value of a data set, found by subtracting the minimum from the maximum.
6th GradeStatistics6.SP.B.5c
What is Range?
The range in statistics tells how far apart the extremes of a data set are. A weather report with highs from 47 to 72 degrees has a wide spread, while a report from 61 to 64 degrees is steady.
Precisely, range = maximum \(-\) minimum. It is one number, in the same unit as the data, and it is never negative. It uses only two values, so one extreme point can change it a lot.
How to spot it
- A question asks how spread out, how variable or how consistent a set of measurements is.
- You are asked for the difference between the highest and lowest scores, prices or temperatures.
- Two sets have the same average and you must tell them apart by variability.
- A graph shows the leftmost and rightmost values and asks about the gap.
The method
- Scan the data and find the largest value, which is the maximum.
- Find the smallest value, which is the minimum, to anchor range in statistics.
- Subtract: largest minus smallest.
- Write the result with the unit of the data, such as degrees, dollars or seconds, and say what a small or large value means for the group.
Range: solved example
Problem
Six days of high temperatures in Boise were 47, 54, 58, 61, 66 and 72 degrees Fahrenheit. A second week in Honolulu had highs of 82, 83, 83, 84, 85 and 86. Compare the ranges.
Solution
Boise: \(72 – 47 = 25\) degrees. Honolulu: \(86 – 82 = 4\) degrees.
The Boise week varies much more. The two spreads are 25 degrees and 4 degrees.
Try it
Question 1
Find the range of 9.5, 12, 7.25, 15, 11.
Show the answer
\(15 – 7.25 = 7.75\).
Question 2
A set has range 0. What does that tell you about its values?
Show the answer
The largest and smallest are equal, so every value is the same.
Range vs. Interquartile Range
The range in statistics uses just the two extremes, so one wild value stretches it a lot. The interquartile range uses only the middle half of the data, so it resists extreme values. Both measure spread, but the second is steadier.
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Whole dictionary: A–Z · 6th Grade · Statistics