The most appropriate measure to compare the consistency of two series is –

Concept

Measures of dispersion are of two kinds. An absolute measure (range, mean deviation, standard deviation) is expressed in the same units as the data, so its size depends on the scale and the average of the series. A relative measure is a pure (unit-free) number obtained by dividing an absolute measure by the average, so it stays comparable even when two series have different units or very different means. Consistency means low relative variability, so comparing the consistency of two series requires a relative measure.

Application

The relative measure built on the standard deviation is the Coefficient of Variation:

CV = (σ / x̄) × 100%

Because σ is divided by the mean x̄, the units cancel and CV is a pure percentage. The series with the smaller CV is the more consistent (more uniform / more stable) one.

Worked example: Series A has mean 50 and σ = 5, so CV = (5/50)×100 = 10%. Series B has mean 200 and σ = 10, so CV = (10/200)×100 = 5%. Although B has the larger standard deviation (10 > 5), B is the more consistent series because its CV is smaller (5% < 10%). A bare comparison of the standard deviations would have given the wrong verdict — that is exactly why a relative measure is needed.

Why the others fail

• Standard deviation — an absolute measure in the data's own units; a larger value can simply reflect a larger mean, not lower consistency.

• Mean deviation — also absolute and scale-bound, so two series on different scales cannot be compared directly.

• Range — uses only the two extreme values, ignores the rest of the distribution, and is still an absolute (unit-bound) quantity.

Cross-check

CV is the only listed measure that is unit-free, so it is the one quantity that stays meaningful when the two series differ in units or means. Hence the Coefficient of Variation is the most appropriate measure for comparing the consistency of two series.