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I need to determine which type of attribute the median of housing price in USD is among the attribute types nominal, ordinal, interval, and ratio.

I would assume, since it is a continuous variable, that the type is ratio, but I am not sure, if i need to treat the median as a 'symbol', and thus a ordinal attribute?

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  • $\begingroup$ What exactly do you mean by a "symbol"? $\endgroup$
    – whuber
    Sep 28 '15 at 19:13
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The correct answer is in fact... Ratio.

I have always hated this terminology, but the word ratio is used for any numerical data measured with respect to some unit of measurements. In this case median house price might be \$200,000 which is to say the value takes a ratio of 200000:1 with the $1 unit of measurement. An important part of ratio measurement, is a unit-less non-arbitrary 0. In this case 0 means specifically no money, no Dollars, Yen, or Euros. 0 is 0.

As per the other answer, in the context of statistical data types nominal is more or less synonymous with categorical, nominal = name. Ordinal is just an ordered nominal variable. And interval is an ordinal variable with constant differences.

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  • $\begingroup$ The terminology was introduced by Stevens who was advised by Garrett Birkhoff. Given that provenance, you wouldn't be surprised to learn that this typology of measurement types is based on a classification of group actions. A "ratio variable" is one where the group that preserves all relevant measurement properties is the multiplicative group of positive reals. Arguably that's the correct one for housing prices (or would be, until you stumble across a negative price resulting from some government support program :-), but the reason is not that there exists a unit of measurement. $\endgroup$
    – whuber
    Sep 28 '15 at 19:11
  • $\begingroup$ @whuber thanks for the background. I certainly like the idea of defining data based on preservation under group actions, this makes a lot of sense. My understanding of the term "ratio" is that we are representing quantities as ratios to other quantities. The one non-canonical part of that procedure is the unit referenced by the ratio, leading to the action of the positive reals. $\endgroup$ Sep 28 '15 at 19:17
  • $\begingroup$ I thought you would appreciate that information. You might be interested in investigating the situation firsthand (especially because so much nonsense has since been written on the subject). The first thing to look at is Stevens' original paper, On the Theory of Scales of Measurement (1946). Then read Velleman and Wilkinson's (1993) reaction, Nominal, Ordinal, Interval, and Ratio Typologies are Misleading. Both are freely available on the Web. BTW, it must have been Birkhoff's father George who was the "late professor G. D. Birkhoff" whom Stevens referred to in 1946. $\endgroup$
    – whuber
    Sep 28 '15 at 19:29
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I'm not sure that I understand your question correctly, but you ask what data type the median is? The same as the underlying variable. Since house price is a nominal variable , the median is also a nominal variable.

An ordinal variable is an ordered categorical attribute - for example if you classified your house prices into percentiles and create an attribute that is

  1. for houses in percentiles 1-40 (low priced)
  2. for houses in percentiles 41-60 (medium priced)
  3. for houses in percentiles 61-100 (high priced)

then the created attribute is ordinal.

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  • $\begingroup$ Although any variable can, for certain analytical purposes, be considered "nominal," it is neither useful nor conventional to conceive of house prices as being of nominal type. $\endgroup$
    – whuber
    Sep 28 '15 at 19:12
  • $\begingroup$ Wow, never knew that. Never saw the "ratio" data type either fwiw, just nominal (continuous or discrete), ordinal, categorical. Learnt something early in the day! $\endgroup$ Sep 29 '15 at 7:12

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