Range and extreme values after PSLE help students see that a data summary can change dramatically when only one observation moves.
The wider transition guide is After PSLE — Should My Child Start Secondary 1 Maths Early?. At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT.
The short answer: range only looks at the smallest and largest values
Range = maximum – minimum.
That makes range very sensitive to extreme values because changing either endpoint changes the spread immediately.
Worked example: one extreme value moves
Data: 4, 6, 7, 9, 10. Range = 10 – 4 = 6.
Now change only the largest value from 10 to 20. The data becomes 4, 6, 7, 9, 20. The new range is 20 – 4 = 16.
One observation changed, but the range increased by 10.
A middle value may change without affecting range
Start again with 4, 6, 7, 9, 10. If 7 changes to 8, the minimum is still 4 and the maximum is still 10, so the range remains 6.
This shows that range ignores most of the internal shape of the data.
Range and mean react differently
An extreme value can move both range and mean, but for different reasons. Range changes because an endpoint moved. Mean changes because the total changed.
The median may stay unchanged if the central position does not move.
For the wider comparison, read Mean, Median, Mode and Range After PSLE.
Worked example: same range, different data
Data set A: 2, 3, 4, 5, 8. Data set B: 2, 2, 2, 8, 8.
Both have range 6, but their internal distributions are very different. Range alone cannot describe the whole data set.
A useful interpretation habit
- Order the data.
- Identify minimum and maximum.
- Subtract minimum from maximum.
- Ask whether one unusual endpoint is dominating the range.
- Compare with mean or median if the question asks for a fuller description.
Independent practice with answers
- Find the range of 3, 7, 8, 12.
- If the maximum changes from 12 to 20, what is the new range?
- If a middle value changes while minimum and maximum stay fixed, must the range change?
- Data has minimum 6 and range 14. Find the maximum.
Answers: 9; 17; no; 20.
Frequently asked questions
Can two data sets have the same range but look very different?
Yes. Range uses only the two endpoints.
Why review this after PSLE?
Because Secondary statistics increasingly asks students to interpret what a summary measure reveals and what it leaves hidden.
Return to the post-PSLE Mathematics hub or WhatsApp eduKatePunggol.
