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I was struggling to find some solution of my problem which is as below:

Let say, I have 20 groups and for each group I have say 10the percentile value. Then is it anyway possible to calculate the 10th percentile for the combined group using those 20 individual 10th percentile?

If there is not any exact solution then any approximation will also be helpful.

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    $\begingroup$ You can say very little when the groups have different sizes. E.g., let one group be enormous and contain 89.9% positive numbers and 10.1% 0's, so 0 is the tenth percentile. If the other groups all have positive values, then the combined 10th percentile is some unknown positive number. If the other groups all have negative values and contain more than 10% of all the data, the combined 10th percentile is some negative value: all you know is that it exceeds the most negative of the individual 10th percentiles. $\endgroup$
    – whuber ♦
    Commented Mar 16, 2012 at 20:48
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    $\begingroup$ To follow up on whuber's comment, if you can give more information about where these groups come from and/or what kinds of structure you expect to see in the data (and especially their relative sizes!) then it might be possible to work something out... $\endgroup$
    – Cyan
    Commented Mar 17, 2012 at 3:09

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Unfortunately, as long as you don't have additional Information, you can't say too much, you can only make probabilistic statements. Let's say, your first 19 groups contain all excactly 10 elements {1,2,3,4,5,6,7,8,9,10} and the twentieth starts at 1000. Somehow combining 20x 1 and the values over 1000 will not represent the wohle group. It could also be that the twentieth group contains 1000 instead of 10 elements, which will make statements difficult.

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