The data is: 2, 5, 5, 9. Kabir says the mode is 9, because 9 is the biggest

Why

Kabir is mixing up two different questions you can ask about a set of numbers: 'which is largest' and 'which appears most often'. The mode answers the second one only — it is the value that shows up the most times in the data, however big or small that value happens to be. In 2, 5, 5, 9, the number 5 appears twice and every other number appears once, so the mode is 5. Test it: change the data to 2, 5, 5, 90 — the mode is still 5, because it is still the value that repeats, and making one number huge did not change that at all. His sister is right: the mode is 5, the most frequently occurring value — 'largest' and 'most common' are different things.