Statistics Fundamentals • Topic 4 of 6

Range

The range measures spread as the difference between the largest and smallest values: range = maximum − minimum. It is quick to compute but uses only the two extremes, so it is very sensitive to outliers and ignores everything in between. A small range means the data is tightly clustered; a large range means it is spread out. On the SAT, range questions test careful identification of the max and min (after any change to the data) and contrast with the interquartile range, which is more robust to extreme values.

✅ Solved examples

1. Find the range of 3, 7, 2, 9, 5.
Max 9, min 2; range = 9 − 2 = 7.
2. Find the range of 12, 15, 11, 20.
Max 20, min 11; range = 9.
3. A set has range 50. The smallest is increased by 10 and the largest decreased by 10. New range?
New range = 50 − 10 − 10 = 30.
4. Find the range of 6, 6, 6.
Max and min are both 6; range = 0.

✏️ Practice — try these, take hints as needed

1. Find the range of 4, 10, 6, 1, 8.
Identify max and min.
10 and 1.
Subtract.
9.
2. Find the range of 25, 30, 22, 40.
Max 40, min 22.
Subtract.
—
18.
3. A set has range 30. The largest decreases by 5. New range?
Lowering the max reduces the range.
30 − 5.
—
25.
4. Find the range of 9, 9, 9, 9.
Max = min.
Difference.
—
0.
5. Find the range of −3, 0, 5, 8.
Max 8, min −3.
8 − (−3).
—
11.

📝 Topic test — 8 questions

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