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Assume I have the following dataset:

building_id    is_business    is_resedential    is_commercial
12             1              0                 0    
13             0              1                 0   
14             0              0                 1
15             1              0                 0
16             0              0                 1
17             0              0                 1

Data description: each category can take 0/1, and each building has one category. So the proportion of business categories is 2/6, residential is 1/6, and commercial is 3/6.

I have a weird question, but I would like to hear your opinion and the possibility of how to interpret it. Does it make sense to calculate the percentile 25, percentile 50, and percentile 75 for each category? Assume we got percentile25=0.0, percentile50=0.2, and percentile75=0.4 for the business category, how would we interpret it?

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  • $\begingroup$ In a sense, you will always get $0$ for the percentile25 on that data for all three indicators. So your question might be better asked about percentile75, which in R would give $0.75$ for is_business, and you need to interpret this as an interpolation estimate from a sample (in this particular case, using an R default type $7$ interpolation method as described by Wikipedia) $\endgroup$
    – Henry
    Oct 23, 2023 at 0:20

1 Answer 1

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If you had a large dataset of buildings where $1/3$ of them are business, then:

  • the 75th and 50th percentiles of the business variable would be 1;
  • the 25th percentile of the business variable would be 0.

So yes, percentiles for 0-1 variables are meaningful. For a small sample with substantial uncertainty about the percentiles, it might even be meaningful to get other percentiles by interpolation which are neither 0 nor 1.

However, I can’t think of a context for a 0-1 variable whose 50th percentile is 0.2 and whose 75th percentile is 0.4: I don’t know any interpolation method for percentiles which could lead to that result. So that particular example may lack a meaningful interpretation; it looks more like an error.

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