This is my first question on Cross Validated here, so please help me out even if it seems trivial 🙂 First of all, the question might be an outcome of language differences or perhaps me having real deficiencies in statistics. Nevertheless, here it is:
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?
Best Answer
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).