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Looking through the various Stack Exchange groups, I think this may be the appropriate group. Apologies if I should have posted this elsewhere.

I have been reading about Scales of Measurement (Nominal, Ordinal, Interval, Ratio)as a way of describing why it’s invalid to do some things to some numbers.

I have two types of numbers which I’m not sure about:

  • Year of publication. It appears to fit in the Interval category (the difference between years is meaningful), but all of the descriptions omit the fact that adding these values is not meaningful. This would also apply to distances and dates in general. That is, would are some interval values addable and some not?
  • Price per item. In all ways this appears to fit in the ration category, but again, adding these numbers is not meaningful. In a sense, price per item would classify as an average, and you can’t do much more with averages.

Do the above categories adequately describe my two examples, or is there another dimension to this? I am aware that Scales of Measurement has had its critics.

Further to this, the year of publication, or any date or any distance, can’t be added, but can be averaged, which is normally obtained by adding.

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A measurement is on the interval scale if differences between values (intervals) are consistent across the scale, e.g. 2009 - 2011 is the same interval as 2019 - 2021. You don't have to be able to add values for them to be on this scale.

A measurement is on the ratio scale if, in addition the above, they have a coherent zero value, and so ratios of values are coherent across the scale, e.g. £110 is 1.1 times £100, and £220 is 1.1 times £200. Ratio-level measurements can also be added coherently.

For your first point, years are a on a ratio scale, but unfortunately the scale measures the time that has passed since the start of the common era (or the birth of Christ, if that's your persuasion). This probably isn't a useful scale, but can be easily transformed to measure the years passed since some other event.

I don't understand your second point. In what sense can you not add prices?

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  • $\begingroup$ In a book shop, title A is priced at £15, while title B is priced at £30. There is nothing to be learned from adding the two prices to give £45. That’s because it is a price per copy, and you don’t know what you have until you first multiply the price by the number of copies bought/sold. $\endgroup$
    – Manngo
    Feb 19, 2022 at 22:56

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