What you’ll learn
Understand variability.
Key idea
Identical observations have no spread; equal centers can accompany very different spreads.
Stacked identical observations do not spread out; variability and center are separate properties even when sample sizes match.
Worked example
Classify examples and non-examples for the concept 'Understand variability'.
Compare A=(12, 12, 12, 12) and B=(3, 9, 15, 21). Classify the claim 'this set has no variability' for B.
- A has identical values (12, 12, 12, 12), so its range is zero.
- B=(3, 9, 15, 21) has the same mean 12 but range 18; equal center does not imply equal variability.
Answer: Non-example — the observations occupy distinct positions.
Quick Check
Classify examples and non-examples for the concept 'Understand variability'.
Compare A=(18, 18, 18, 18) and B=(9, 15, 21, 27). Classify the claim 'this set has no variability' for A.