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I haven't be able to find an answer to this so any suggestions would be really useful.

I've been asked to post stratify a survey and I'm currently trying to do this for gross personal income. The sample respondents ticked a box for the income band they reside in, which is as follows:

  • Below 20,000
  • 20,000 - 49,999
  • 50,000 - 79,999
  • Above 80,000

I've obtained income data from the national statistics database, however, they only release the income distribution at this geography in (pretty much) deciles (10, 20, 25, 30, 40, 60, 70, 75, 80, 90) (I also have the mean and median values). Taking the first category as an example, I know that 20,000 lies somewhere between the 30th and 40th percentiles. Am I able to take this quite detailed information about the income distribution, estimate the points in between, and then attempt to work out the percentage of the population falling between the income bands in the survey?

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    $\begingroup$ For what use do you need this (yes, I think that info will inform what answers are most useful). Do you have in mind some theoretical clas of distributions to use? Or will it do with some empirical approximation? There is a complete book about income distributions: "Statistical Size Distributions in Economics and Actuarial Science" by Kleiber & Kotz. Do you want to use one of those theoretical distributions? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Feb 9, 2015 at 13:33

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