A hard question on averages for P5–P6, with a step-by-step solution, diagrams and the answer. Averages appear in the Hua Xia Cup's P4 and P5 first rounds, qualifying rounds and finals.
The question
A teacher works out the test average for a class of 24 (out of 100) and gets 64.
Then she finds one pupil's mark was copied wrongly as 36.
Once it is corrected, the class average becomes 65.
What did that pupil actually score?
Show the hints (3)
💡Hint 1: Only one mark changes. By how much does the class total change?
💡Hint 2: The average moves by 1, and there are 24 pupils.
💡Hint 3: The class total changes by (change in average × number of pupils), all of it from that one pupil: true mark = the copied mark plus that change.
Worked solution
Have a go first, then read the solution step by step.
1.The average goes from 64 to 65: as if each pupil changed by 1, so the total changes by 1 × 24 = 24.
2.All of that change comes from the one pupil: the true mark is 24 more than the copied one.
3.True mark = 36 + 24 = 60.
⚠️Common mistake: thinking the mark is only 1 out. The average moves by 1, but the total moves 24 times as much.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download