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I have some census data on income I would love to analyze. But income, in the data, is split into different income groups, each group is a column containing the number of people in an area that earns A to B. If my explanation doesn't make any sense please look at the table below.

So basically I want to get the average income for an area. Can this even be done with data like this?

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    $\begingroup$ Back in the old days, when people summarized data to save space and computational effort, there were many well-known methods to cope with this problem. Kendall's Advanced Theory of Statistics describes Sheppard's Corrections, which I have explained in the thread at stats.stackexchange.com/questions/60256 . $\endgroup$
    – whuber ♦
    Commented May 25, 2016 at 18:09
  • $\begingroup$ O My Word!! whuber that is awesome. With my limited knowledge of stats it is taking me some time to understand Sheppard's Corrections. But it is absolutely wonderful. Thanks $\endgroup$
    – Jcstay
    Commented May 27, 2016 at 9:36

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You will probably not be able to get a good average income for an area without getting more specific data, but you might be able to attack this problem by making some approximations and checking them/following up.

Some assumptions you could make that come to my mind would be:

  1. Assume that on average most people in any given bin is at the average for that bin.
  2. If you want to be more slick you might have a better distribution within each bin. You could use this calculate the average in each bin and then you would be done. (eg maybe the distribution of data is log-normal)

The trick is if you can get the mean within a bin for an area you can then perform a weighted average. Most of the methods I listed would assume independence of the bin average as a function of area, but you might find that unacceptable. In that case you would need to try to reconstruct a function that calculates the average bin income as a function of area, which seems more ambitious than your original project.

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  • $\begingroup$ Thanks, I agree this seems to become allot bigger than I thought. But there is nothing as exiting as a good challenge. Any way thanks for the great advice, your helping me allot to understand these type of thins better. I'm also going to look at Sheppard's Corrections as pointed out by whuber $\endgroup$
    – Jcstay
    Commented May 27, 2016 at 9:40

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