中等MATH-STAT-012
A student says, 'The class average rose, so every student improved.' Why is this an abuse of the average?
A. The median must have fallen
B. An average cannot rise
C. The standard deviation is zero whenever the mean rises
D. An average can rise even if some students scored lower✓ 答案
解說
The mean is a single summary. Large gains can outweigh other students' losses, so a higher mean does not describe every member of the class.