In Romania, the median net income in 2013 was 284 EUR/month, the average net income (unfortunately, in 2014, not in 2013 as the previous data point, but lets assume the same amount for 2013 for simplicity) was 423 EUR/month.

Is it possible from these 2 data points to compute the percentile rank of a net income of, lets say, 2000 EUR/month?

I've googled for an algorithm to compute this, but unfortunately I couldn't find any.

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  • $\begingroup$ Not without a model for the distribution. The median gives you one point on the quantile function and the mean is a related integral, but any number of quantile functions are consistent with that information. $\endgroup$ – Nick Cox Mar 5 '15 at 10:39

In short, no. It could be consistent with a wide variety of different values.

If you make some assumptions about the distributional form, then in some cases you could estimate it, but you'll be almost wholly reliant on the correctness of the assumption and being without any data to check it against, it would seem like a highly risky thing to do.

Sometimes income is modelled using a lognormal distribution, for example, but it's at best a very rough approximation, and it isn't always suitable. For example, sometimes income distributions are multimodal, but most of the common models are not.

If you have some other information about Romanian income distribution, you may be able to do better.

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    $\begingroup$ +1, And sometimes Pareto, Dagum, Singh-Maddala distributions, etc., etc. $\endgroup$ – Nick Cox Mar 5 '15 at 10:40

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