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Given computed values for a box plot (min, lq, median, uq, max) and original raw data size is it possible to merge that with raw data.

given:

box1 = [min:1,lq:2,median:5,uq:8,max:10]
size1 = 50 #size of dataset that gave me the box1 calculated values
data2 = [1,1,6,...]

How can I combine both into a new box plot. Is this possible, or do I need the original raw data and have to merge it with the new raw data before calculating the box plot values.

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  • $\begingroup$ So you want a plot that shows a boxplot plus the original raw data at the same time? In what package? (In R, I've come to really like the beanplot package, using jitter to display the raw data. $\endgroup$ – Wayne Jun 6 '12 at 19:41
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You need the raw values because otherwise how could you infer the combined order statistics that you need. You need to know exactly how the data points are interwoven when they data are combined.

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  • $\begingroup$ That's what I thought, just wanted to make sure. Is there something similar to the box plot that would let me do this. $\endgroup$ – Kassym Dorsel Jun 7 '12 at 13:53
  • $\begingroup$ Are you familiar with stem-and-leaf diagrams? $\endgroup$ – Michael Chernick Jun 7 '12 at 13:55
  • $\begingroup$ I originally chose the box plot since it can take huge amounts of data (>10000). I was looking for an easy way to aggregate the raw data and flush it, while still conserving it's value $\endgroup$ – Kassym Dorsel Jun 7 '12 at 16:28
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    $\begingroup$ Despite the negative conclusion of this reply, Kassym, what you want can be done: see stats.stackexchange.com/questions/7959 for some pointers. The principal ideas are (1) accept the possibility of a little error in the results (that's the force of Michael Chernick's remark) but (2) create a data structure that enables reasonably accurate updating of the quartiles (or other percentiles) as new data come in. $\endgroup$ – whuber Jun 7 '12 at 19:46

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