# "Variability of" vs "variability in"

How to choose between "variability of something" and "variability in something"?

Both forms appear to be widely used, e. g. Google: "variability of this" (21m results) and "variability in this" (27m results). However, in some more specific cases, one form is used exclusively, e. g. "variability of this factor" (500k results) and "variability in this factor" (2 results). On the other hand, the phrases "variability of the data" and "variability in the data" are used with comparable frequencies.

• In the fields of statistics and data analysis, the term used in such contexts isn't "variability" but "variance," so your research should start by using the term "variance" rather than "variability" as any hits you got that use "variability" are going to refer to contexts that don't refer to data or do but are written by laypeople, people who lack sufficient expertise to use the proper terminology. Also, for more grammatically reliable results, results just from published works rather than the whole Internet horde, use Google Ngram (books.google.com/ngrams), not a simple Google search. Commented Jun 10, 2021 at 2:29

How to choose between "variability of something" and "variability in something"?

Both In and Of are prepositions therefore depending on the noun following "variability in or of may be used.

variability of this factor"

In this case of is the preposition for a number and factor is another name for number.

factor noun (NUMBER) of preposition (AMOUNT) used after words or phrases expressing amount, number, or a particular unit:

In this example

Both sides agree there is year-to-year variability in hurricane activity.

what is actual meant, is there is variability involved with the activity of Hurricanes Both sides agree there is year-to-year variability INVOLVED with hurricane activity.

In this case in is the preposition to indicate involvement.

in preposition (INVOLVED)

also variability can be used without in or of

The cross-co variance revealed several features of the variability that reinforced other observations

Link C.E.D Both sides agree there is year-to-year variability in hurricane activity.

I have found in Gngram that you can say variability of response and variability in response (the latter is clearly more commonly used).

Both variability in temperature and variability of temperature exist as again Gngram shows, with not much difference in frequency.

Therefore, I doubt that it is the noun following the structure

VARIABILITY + ON/IN + NOUN

that determines the use of in or of.

Note that "variability in" is preferably used with a singular noun (a common feature like shape, age, or an abstract noun like activity, productivity). Here the stress falls on the noun phrase (in length) showing 'which kind of variability the speaker refers to'. See for example:

The tongue presents little variability in length, being short and compressed, with a blunt tip, which is never protruded beyond the incisors.

"Variability of" can be followed by a noun in both singular and plural and shows that variability is a characteristic possessed by the noun that follows. See for example:

A transformation which is sometimes rapid, sometimes slow, but always continuous, is wrought by the reciprocal action of the innate variability of plants and of the variability of the external factors.

(both examples are from yourdictionary.com).