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Quartiles of ungrouped data 
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#1
Feb2512, 09:46 AM

P: 28

From the question, is the way to find Lower Quartiles and Upper Quartiles correct? I have seen books taking the 3rd and 8th (from the question) as Lower Quartiles and Upper Quartiles respectively. Which should be the correct Quartiles?



#2
Feb2512, 05:02 PM

P: 2,504

[itex]P[X < x] \leq k/n; P[X\geq x] \geq 1  (k/n)[/itex] So by the first inequality if x is ranked 5th highest point out of 100 data points, then k=95 and P=0.95 which is the 95th percentile. It seems you want the upper quartile (top 25%), and lower quartile (bottom 25%) . The meaning of the term 75th percentile is that 75% of all data points are less than the lowest data point of the upper quartile. 


#3
Feb2512, 07:19 PM

P: 28

Based on the attachment http://www.physicsforums.com/attachm...5&d=1330184818, is this the correct way to interpret quartile?



#4
Feb2512, 08:51 PM

P: 2,504

Quartiles of ungrouped data
If you type out what you're doing, I can tell you more, You seem to be doing it correctly. For an even number of values, some people use k+1, as you have, so quantile boundaries do not fall on data points. The value of your median is then 5.5 and the quartile boundaries would be calculated using 2.75. So 5.5  2.75 = 2.75. Your answer could be this or 2,25. I'm not sure which. 


#5
Feb2512, 09:33 PM

P: 28

There are 10 data values in my attached example.
{51, 55, 57, 61, 62, 67, 70, 72, 73, 74} Q_{1} = 56.5 Q_{3} = 72.25 But Q_{3} = 72 instead 


#6
Feb2512, 10:08 PM

P: 2,504




#7
Feb2712, 01:39 PM

P: 2,504




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