T he outcome of a standardized test is an integer between 151 and 200, inclusive. The percentiles of 400 test scores are calculated, and the scores are divided into corresponding percentile groups.
QA: Minimum number of integers between 151 and 200,inclusive, that include more than one percentile group
QB: Minimum number of percentile groups that correspond to a score of 200
Hi, can someone please help with this problem? I’m having a hard time understanding the solution given in the book.
Hi, I will try my best to explain a simple manner fingers cross
Firstly, let me draw an example (outside of the question):
Lets say we have three scores: 3, 6, 9. If I were to ask you what the 50th percentile (median) of this data set is, it easy, 6. But if I were to ask you what the 25th percentile or the 6th percentile is, its not very obvious but its 3. Why? Because that’s the only data point we have. This example helps explain QA. If we have only 3 scores but need to fit it into a 100 percentile scale, the number 3 is the 1st, 2nd, 3rd…49th percentile, the number 6 is the 50th percentile, the number 9 is the 51st, 52nd…100th percentile. So here we can see 3 and 9 is included into more than one percentile group, while 6 is exactly in one percentile group.
Now going to the question, if we assume that all 400 test takers scored 151, 152 and 153 (no other scores), we would get the same picture, 151 is the 1st~49th percentile, 152 is the 50th, and 153 is the 51st~100th. In this case, 151 and 153 is in more than one percentile group.
And because we only have 50 scores available (151 ~ 200), to fit this into a 100 percentile scale entails at least one integer occupying more than one percentage group.
Furthermore, if all the scores are 151,152,153, then no scores of 200 fall within any percentile groups because no one scored a 200, therefore the minimum is zero.
Thus the answer is QA.
Since my reply is already prolix (GRE vocab!) I will add on another bit : if the question were to be altered to say: “the scores range from 151 ~ 250, we would have 100 available scores” then the minimum number of integers to occupy more than one percentile group will be zero. Why? because there could be a case where every score from 151 to 250 is in the data set and in that case 151 is the 1st percentile, 152 is the 2nd…250 is the 100th.
Hope this clarifies!