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image 1

above question is copied from http://web.mnstate.edu/peil/MDEV102/U4/S36/S363.html

So our n = 10

Hence we have (10+1)*0.25th = 11*0.25th = 2.75th

2.75 places along the set of numbers is somewhere in between here 5 and 7

(7-5)*0.75 = 1.5

so 5+1.5= 6.5

Like wise Q3=15.75

I have calculated Quartiles using above method (method in image 1) and the answers are correct. but when I used formulas it gives me different answers for the above data set in image1. I am confused with this. What did I do wrong? Can anyone explain? Using the formula gives sometimes different answers why? which method is correct to use?

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    Hi, it's best to get out of the habit of writing e.g. $10+1=11*.25\ldots$ because this is not a true statement. $10+1=11$ is true. Then $11*.25=2.75$ is a separate statement also true. But to write in one line you have written $11=2.75$, which is untrue. – 2017-01-20

2 Answers 2

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There is no universal agreement on a "correct" definition of quartiles for a discrete data set. Wikipedia gives three different methods, which each will give different results.

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You need to add $1/2$ instead of adding $1$ and then dividing by $2$. Once you're calculating a quartile, as you are now, your method of adding $1$ then dividing by $4$ breaks down. You're adding a quarter, which is incorrect.

You should always be adding $1/2$ because you are allowing for the fact that the boundary around any number is $1/2$ of a place either side of the centre of that number.