In Quant tickbox quiz #13, question 15 reads: “A scientist recorded the heights of
500 people with such precision that no two heights were the same. Is the number of people in the
11th percentile greater, smaller or equal to the number of people in the 45th percentile?”
To solve this, Greg divides 500 by 100 and shows that there will be 5 person per bins. My question is: isn’t that always the case? Like, by definition, the same number of people will be contained in each percentile, regardless of having 500, 501, 502 obs, etc. Or not?
Can you divide 502 into 100 equal bins?
No you cannot; however, my reasoning is that 13 is also not divisible by 4, and yet you still can divide the dataset into 4 groups with an equal number of observations using quartiles. Say, you have a list of all positive integers from 1 to 13. Then, Q2 is 7, Q1 is 3.5 and Q3 is 10.5. The data will have been divided into 4 bins of 3 observations each, and this is because the number 7 is “discarded” as the median. Why does this rationale not apply to percentiles?
No? The number of elements in each of the four quartiles isn’t the same.
I am sorry, maybe I am missing something. The list is:
1 2 3 4 5 6 7 8 9 10 11 12 13
Q2: 7
Q1: 3.5
Q3: 10.5
1st quartile: 1 2 3
2nd quartile: 4 5 6
3rd quartile: 8 9 10
4th quartile: 11 12 13
Or did I do something wrong?
In this video (Quartiles), minute 2:30, Greg refers to the list 1 2 3 4 5 6 7 and says “These are boundary lines; the Q1, Q2 and Q3 are boundary lines; so, in the 1st quartile, there is only the number 1; in the 2nd quartile, only number 3; in the third quartile, only 5, and in the last quartile, only 7”.
So I get the sense that Q1, Q2 Q3 do not “belong” to any bin, since it is explicitly said that “the first quartile contains only 1 and the second contains only 3”
That is a little awkward - and that’s why GRE is pretty much not going to have you deal with problems where you need to find quartiles and the number of terms in the list is not a multiple of 4.