pachaquis3s

2022-06-25

How do I calculate the quartiles for this problem?
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 ${Q}_{3}$

Belen Bentley

Expert

So the formula to calculate Quartiles is
Q1 =$\frac{1}{4}\left(n+1\right)$
and
Q3 =$\frac{3}{4}\left(n+1\right)$
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

anginih86

Expert

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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