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I have the following list of numbers, and I'm trying to calculate the quartiles:

2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9

I'm running into a bit of confusion because the median turns out to be 7. Now I don't know how to demarcate the lower group from the upper group since there are a whole bunch of 7's. Consequently, I don't know how to calculate $Q_1$ and $Q_3$.

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2 Answers 2

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So the formula to calculate Quartiles is

Q1 = enter image description here

and

Q3 = enter image description here

So our n = 16

Hence we have 16+1 = 17*.25 = 4.25

4.25 places along the set of numbers is somewhere inbetween here 5 and 7

so if we split the numbers between 5 and 7 into 4 pieces i.e.

5 5.5 6 6.5 7

We can calculate .25 or 1/4 along the way of our little number line we just created is 5.5

Hence Q1 = 5.5, with this method you should be able to find Q3 which is 8.75

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  • $\begingroup$ Your answer doesn't agree with the other answer posted by EpicGuy. It also doesn't agree with my original source from where I took the problem. I like your method, but the other answer is the correct one. I'd like to know how to get the correct answer using this method. Could you please double-check this? Thanks. $\endgroup$
    – Joebevo
    Sep 10, 2013 at 11:36
  • $\begingroup$ BTW, I am the OP. I was finally able to log into my own account. $\endgroup$
    – Joebevo
    Sep 10, 2013 at 11:38
  • $\begingroup$ @Joebevo You can use a calculator to check if you like here alcula.com/calculators/statistics/quartiles i.e. the answer is correct $\endgroup$
    – Sim
    Sep 10, 2013 at 11:39
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you just divide the list into quarters.

First divide into half... 2 4 4 5 7 7 7 7|7 7 8 8 9 9 9 9

Then quarters... 2 4 4 5|7 7 7 7|7 7 8 8|9 9 9 9

So Q1 is average of 5 and 7 which is 6, and Q2 is average of 8 and 9 which is 8.5

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