# Quartiles

Quartiles - I thought this was a really easy topic but I’m afraid I’m missing something. Below, I could guess D (the correct answer) based on dividing 24 (values) by 4 (for quarters) but I would have thought the range would have to be actual numbers from the given set, like 27.5 to 36.8 from the data, not the numbers in answer D. Anybody have any suggestions? (based on a SASF practice problem) 8.2 21.4 26.9 31.5 39.9 12.3 22.0 27.1 33.3 44.5 15.1 22.6 27.5 33.8 47.2 16.6 23.4 28.6 36.8 50.0 17.4 26.7 29.2 39.7 Then, they ask which is the closest range of the second-highest quartile: A. 8 to 21.7 B. 17.1 to 23.0 C. 31.5 to 40.0 D. 27.3 to 35.3 (correct)

Atleast they sorted and gave us the data set :-)) Highest-Quartile: 36.8 to 50 2nd-Highest-Quartile: 27.5 to 33.8 3rd-Highest-Quartile: 22 to 27.1 Last-Quartile: 8.2 to 21.4 So the answer should be D since they have asked for the closest answer and we don’t need to worry much on searching for the exact matching range… but just to make sure, see to it that ‘35.3’ given in the option D does not fall under any of the other quartiles. The highest quartile starts from 36.8 (so 35.3 falls outside the top-quartile) so we are good to select option D as a final answer. - Dinesh S

Thanks. So, that’s it? Where do the get the exact numbers for answer D? Are they doing some interpolation or just trying to trick us?

actually, this is how you do this (you’re right you have to interpolate), pos = (n+1)*(percentage/100), something like this, in essence, they’re asking for the range 50th-74th, so you have 2 pos 1. pos(50) = (24+1)*(50/100) = 12.5 -> 12th item + 0.5*(13th-12th) = 27.1 + 0.5*(0.4) = 27.3 2. pos(74) = (25)*(74/100) = 18.5 -> 18th + 0.5*(19th-18th) = 33.8 + 0.5*(3) = 35.3 hence the answer is D…

Interesting liaaba, I didn’t know we had a formula for quartile calculations… Thanks!! Thought I intuitively got the answer correct, this will surely help us in precision (interpolated calculation) and save us some clock on the exam day. It’s in my formula sheet now… ----------------------------------------- pos = (n+1)*(percentage/100) ----------------------------------------- - Dinesh S

anyone who have appeared for level 1, is this a typical exam problem. It is time consuming, but at the same time I fail to see any logic applied apart from direct mathematical application. Any thoughts.

Liaaba, why is the 2nd highest quartile 50th to 74th instead of 51st to 75th?

because 100 to 75 is the 1st (Top Most) Quartile and Quartiles are nonoverlapping so the next quartile has to start from 74 lowering down to 50 … the 3rd from 49 lowering down to 25 and finally the last quartile from 24 to 0 Hope this makes sense? - Dinesh S

But why is the top quartile 100 to 75, and not 100 to 76?

because 100-75 is 25 and 100 - 76 is 24 (and we would be undercounting the quartile if we did this…) - Dinesh S

76-100 inclusive is 25. 75-100 inclusive is 26.

To avoid confusion, you can number them from zero to 99: Q1 = 0 - 24, Q2 = 25 - 49, Q3 = 50 - 74 Q4 = 75 - 99 The third quartile starts on the 50th item. If the number of items is even (say 100), then it starts on the value located in the 50.50 position (100 + 1)* 0.50 = 50.50), not the 50th position. Dreary

Now I see that you just have to separate the data in four equal sets and then take the midpoints (simple averages) of the highest number in the lower quartile with lowest number in the quartile above it! This gives the exact numbers in answer D. Don’t worry people - this is not the only problem I’ve been working on this week! I hope this helps someone.

So there is this formula posted above that gives a single number for the quartiles (more generally, any quantile) but there are about 5 posts below and a bunch above that give quartiles as ranges. A quartile is ONE number not a range or an interval or 2 numbers…

Joey is so right. The question is (in mathematical point of view) a bad one. If I was txcany, i would change the question supplier…