SCALES OF DATA AND PERMISSIBLE DESCRIPTIVE STATISTICS

The table below shows different descriptive measure and the scale for which they are permissible. Binary variables are technically on the nominal scale, but allow for some descriptive measures that other nominal scaled variables don’t.

	Binary	Nominal	Ordinal	Interval	Ratio
Percentiles	NO	NO	YES	YES	YES
Mean	YES[1]	NO	NO[2]	YES	YES
Median	NO	NO	YES	YES	YES
Mode	YES [3]	YES	YES	YES[4]	YES[4]
Minimum and Maximum	NO	NO	YES	YES	YES
Range	NO	NO	NO	YES	YES
Standard Deviation	YES	NO	NO	YES	YES
Variance	YES	NO	NO[2]	YES	YES
Interquartile Range	NO	NO	NO	YES	YES

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[1] It is the proportion

[2] But often done for Likert scales and in the absence of higher quality data

[3] It is the absolute majority

[4] But useless if there are too many different values