300 test results are integers ranging from 15 to 75, inclusive. Dominick’s result is clearly in the 80th percentile of those results, not the 79th or the 81st.
Quantity A: Number of other test results in the same percentile as Dominick’s
Quantity B: Maximum number of other test-takers with the same result as Dominick
Compare Quantity A and B.
Since the number of test results is divisible by 100, the percentiles cleanly divide the total into 100 percentile groups of 300 ÷ 100 = 3 results each. That is, there are 3 results in each percentile. So 2 other results are in the same percentile as Dominick’s. Quantity A is 2. Dominick’s result is clearly in the 80th percentile, not the 79th or the 81st. So it must be possible to distinguish the 80th percentile (that group of 3) from the “next-door” percentiles. Say Dominick got a 58. How many other people could have gotten a 58? Maybe no one, maybe one, maybe two — but if three other people got a 58, then you’d have a total of four people with the same result. In that case, it would be impossible to assign Dominick’s result definitively to the 80th percentile and not the neighboring percentiles. So the maximum number of other test-takers with the same result as Dominick is 2. Quantity B is also 2.
Is this a normal distribution? If this was a Normal Distribution would this be a valid explanation? I mean, in a normal distribution, wouldn't most of the 300 test scores be concentrated around the mean, so each of those percentile points around the mean would have more of those 300 test scores?
How do I picture this in a graph? The frequency of the test scores in Y-Axis and the integers ranging from 15-75 along the X-Axis? If that's the case, then wouldn't the graph be a flat line, because every score has only 3 test-taker (frequency).
- In general I want to know, how can we know, that as there is 300 test results, they must divide into equal percentile blocks.