There are $17$ students in Marek's class, and all of them took a test. Marek's score was $17$ points higher than the arithmetic mean of the scores of the other students. By how many points is Marek's score higher than the arithmetic mean of the scores of the entire class? Justify your answer.
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Tags: trivial
Batlete
22.05.2023 01:37
There are $16 $ unnamed students, as well as Marek, in the class of $17. $ On average, say each student (excluding Marek) scored a number, which we'll call $x. $ The total score of the class is $16x +(x+17)=17(x+1) $. So, each student (including Marek) scored an average of $x+1 $ points. Since Marek's score was $17 $ above $x $, his score is $16 $ above the class average, so the answer is $\boxed{16}. $
joshualiu315
22.05.2023 01:57
Assume all the other students got $0$. Their mean is $0$ which means Marek scored $17$. The mean of all $17$ students is $1$, so our answer is $16$.
KangarooPrecise
22.05.2023 03:33
There is 17 students and Marek's score is 17 higher, we can use 0 as the mean for all the other students, thus the answer is 16