13+ Averages Maths Question from Harrow School

In this video, Singapore Maths Academy breaks down a multi-part averages question from a Harrow School 13+ entrance paper that tests students on mean, median, mode, and range — as well as their ability to reason with statistical data.

The question presents a list of marks out of 20:
13, 9, 14, 17, 20, 15, 18, 14
and asks students to:

• (a) Calculate the mean mark
• (b) Identify two marks that could be removed without changing the mean
• (c) State the median and the mode
• (d) Compare with a new set of results from a re-test using summary data (mean = 13.5, median = 17, mode = 8, range = 15) and evaluate whether the class did better

We solve the problem step-by-step, demonstrating how to approach each part clearly and interpret the results meaningfully — a key skill for entrance exams like the Harrow 13+, where mathematical reasoning is as important as calculation.

This question not only tests numerical fluency, but also data literacy — the ability to justify and explain based on mathematical evidence. A must-practice topic for any student aiming to pass selective senior school entrance exams confidently.