The range is the crudest measure of spread: greatest value minus least value. Because it depends only on the two extreme numbers, it is extremely sensitive to outliers — values that sit far from the rest of the data. The GRE exploits this contrast constantly: an outlier can swing the range and the mean dramatically while leaving the median and the mode untouched. That is the whole reason the median is called "robust". When a question adds or removes a value, ask which statistics it can actually reach: a new value between the current minimum and maximum leaves the range unchanged, while a value outside that band expands it. A subtle point worth internalising — adding the same constant to every value shifts the mean and median by that constant but leaves the range and standard deviation completely unchanged, because spread does not care where the data sits, only how stretched out it is.
✅ Solved examples
1. Find the range of 14, 9, 27, 5, 18.
Greatest = 27, least = 5. Range = 27 − 5 = 22.
2. A set is 20, 22, 25, 28, 30. A value of 90 is added. What happens to the range and the median?
Range was 30 − 20 = 10; now 90 − 20 = 70, so it jumps by 60. Median was 25 (3rd of 5); with six values it is the average of 25 and 28 = 26.5. The outlier hammers the range but barely moves the median.
3. Every value in a data set is increased by 7. What happens to the mean and the range?
The mean increases by 7 (it shifts with the data). The range is unchanged: both the max and the min rose by 7, so their difference is identical.
4. Quantitative Comparison. Set S = {3, 4, 5, 6, 7}. Quantity A: the range of S. Quantity B: the range of S after each element is multiplied by 2. Which is greater?
Range of S = 7 − 3 = 4. After doubling, S = {6, 8, 10, 12, 14}, range = 14 − 6 = 8. Multiplying scales the range by the same factor. Quantity B (8) > Quantity A (4). Answer: B is greater.
✏️ Practice — try these, take hints as needed
1. Find the range of 45, 12, 67, 23, 8, 51.
Identify the largest and smallest.
Max = 67, min = 8.
67 − 8.
59
2. A set has range 40 and minimum 12. What is its maximum?
Range = max − min.
40 = max − 12.
Add 12 to both sides.
52
3. To {10, 14, 18, 22} you add one value and the range stays 12. Give one value that works.
Current range = 22 − 10 = 12.
Any new value must not fall outside 10–22.
Pick anything from 10 to 22 inclusive.
Any value from 10 to 22 (e.g. 16)
4. Each value of a set is decreased by 5. The old range was 30. New range?
Subtracting a constant shifts all values equally.
Max and min both drop 5.
Their difference is unchanged.
30
5. Set {2, 4, 6, 8, 100}: which changes more when 100 is removed, the mean or the median?
Mean uses every value; the median is positional.
Old mean = 24, new mean = 5.
Old median = 6, new median = 4.
The mean changes far more (24 → 5) than the median (6 → 4)
📝 Topic test — 8 questions
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