30
$\begingroup$

In population statistics, are variation and variance the same terms? If not, what is the difference between the two?

I know that variance is the square of standard deviation. I also know that it is a measure of how sparse the data is, and I know how to compute it.

However, I've been following a Coursera.org course called "Model Thinking", and the lecturer clearly described variance but was constantly calling it variation. That got me confused a bit.

To be fair, he always talked about computing variation of some particular instance in a population.

Could someone make it clear to me if those are interchangeable, or perhaps I'm missing something?

Improve this question
$\endgroup$
6
  • 7
    $\begingroup$ Variation, unlike variance, is not the name of some specific quantity (however, Coefficient of variation is). It is a generic term, like variability. It is just amount of variability which can be measured by various quantities (most popular of them being variance). $\endgroup$
    – ttnphns
    Mar 1, 2014 at 7:36
  • $\begingroup$ So basically you are saying that Variance is a real statistical term with a formal model standing behind it, but variation is just a word describing relation between expected & real data? $\endgroup$
    – ŁukaszBachman
    Mar 1, 2014 at 7:42
  • $\begingroup$ Right - I changed that :) $\endgroup$
    – ŁukaszBachman
    Mar 1, 2014 at 7:46
  • 2
    $\begingroup$ Variance has a formula. Variation has no one formula, it is a generic term. Both variance and variation can be 1) a statistic describing a sample, 2) a parameter describing a population, 3) a statistic as an estimate of the correstonding parameter $\endgroup$
    – ttnphns
    Mar 1, 2014 at 7:46
  • 4
    $\begingroup$ Another analogue here is "spread." There isn't a formal equation for calculating "spread," although it's appropriate to say that "variance" is a measure of "spread." I think in this context "spread" and "variation" are equivalent. $\endgroup$
    – David Marx
    Mar 1, 2014 at 8:25

2 Answers 2

Reset to default
23
$\begingroup$

Here's a full wikipedia article discussing this topic: http://en.wikipedia.org/wiki/Statistical_dispersion

As described by others in the comments here, the short answer is: no, variation $\ne$ variance. Synonyms for "variation" are spread, dispersion, scatter and variability. It's just a way of talking about the behavior of the data in a general sense as either having a lot of density over a narrow interval (generally near the mean, but not necessarily if the distribution is skewed) or spread out over a wide range. Variance is a particular measure of variability, but others exist (and several are enumerated in the linked article).

Improve this answer
$\endgroup$
2
14
$\begingroup$

Variation may be understood best as a general term for a class of different concepts, of which $(\sigma^2)$ is only one. Levine and Roos (1997) also consider $(\sigma)$ a variation concept, among others.

To demonstrate why the distinction might be important, compare also the $(\frac\sigma\mu)$, and the mathematical concept, total variation, which has several definitions unto itself. Then there are all manners of qualitative variation, which are mentioned in the Wikipedia article @DavidMarx linked. These pages corroborate his answer BTW; statistical dispersion or variability are better synonyms for variation than variance, which is clearly not so synonymous.

BTW, here's a cool GIF of one kind of total variation: the length of the path on the $y$ axis that the red ball travels.

Definitely not the same as variance!

Reference
Levine, J. H., & Roos, T. B. (1997). Description: Numbers for the variation. Introduction to data analysis: The rules of evidence (Volume I:074). Dartmouth College. Retrieved from http://www.dartmouth.edu/~mss/data%20analysis/Volume%20I%20pdf%20/074%20Description%20%20Numb%20for.pdf

Improve this answer
$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.