# Density function from percentiles (P10, P25, P75, P90, mean and median)?

I have percentile data (P10, P25, P75 and P90) for a variable.
I also have the mean and median for each group:

group    mean   median  P10     P25     P75     P90
1        30100  26200   19900   22500   32800   44200
2        38700  36600   28000   31500   44000   52100


How do I:

1. Create a probability density function based on these variables.
2. Use that function to give me the % in specific step intervals? (I.e. answering the question: How many out of 100 are in the 30000-31000 interval for group 2?)

Thanks.

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Do you assume any underlying distribution of your variable -- like a normal distribution? –  krlmlr Feb 23 '12 at 10:42
This is income data per occupation in a single country so I'm not sure what to assume? Thanks. –  dani Feb 23 '12 at 11:49
Then you'll have to assume a distribution in the first place. Otherwise there's no way to tell which PDF fits the data best. -- Also, isn't P50 supposed to be the same as the median? –  krlmlr Feb 23 '12 at 12:09
OK, I guess I should assume a normal distribution then? Does that make sense looking at the data? And of course you're right, it should be P75 instead of P50!! –  dani Feb 23 '12 at 12:20
Then: What is P100, the maximum in each group? Do you have this data? –  krlmlr Feb 23 '12 at 12:27