Measurement scale

A measurement scale tells you which operations preserve meaning. The values may be stored as numbers, but storage format does not decide the scale.

The mean of invoice IDs is nonsense. Coding the three customer segments as 1, 2, and 3 does not create a quantitative distance. The median review priority may identify a middle ordered category, but a difference of one code is not a measured amount.

Settlement days support more operations. Forty days is ten days longer than thirty, and—under the stated time origin—twenty days is twice ten. That does not make every ratio interpretation useful; it only makes the arithmetic meaningful.

Calendar dates provide the business-data contrast. Juniper's packet defines issue date even though the learner extract stores only the resulting duration; generically, the number of days between January 5 and January 15 is meaningful, but a calendar's origin is conventional: one issue date is not meaningfully “twice” another. Dates therefore support differences without turning their stored date codes into ratio-scale amounts.

Match the summary to the question

Nominal variables invite counts and proportions. Ordinal variables can use ordered counts and positional summaries. Interval and ratio variables may support means and standard deviations when their distribution and purpose make those summaries informative. Always preserve the data definition: an allowed operation can still answer the wrong business question.