How do we interpret variance?

[oktavian]

Seems shocking to ask this question after studying levels 1 and 2, but I guess the more basic the knowledge gap, the faster it should be filled.
How do we interpret variance? I understand that a larger variance means more volatility than a smaller variance – this is an ‘ordinal’ quality (rememeber NOIR? haha) but beyond that, what quantitative meaning does it have? Or how is it used?
Standard deviation seems to tell us a lot more about the probability of deviation from the mean (e.g. 68% of returns should be within ±1SD for gaussian distributions), so why do we still hear about Variance so much? Why not just use SD and be done with it?
Does variance have more value in non-normal distributions? How have I come this far without discovering it?
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Just to clarify (for people who don’t read the details question), I AM already clear on:
- how to calculate variance
- the ordinal quality of variance (i.e. bigger variance means more volatility / “risk”)
- the quantitative meaning of standard deviation (e.g. 68% of normally distributed results will within ±1 SD etc.)

 

[Harrogath]

Really good question…
What I know is that we cannot interpret variance because it has no sense. For example you can have a variance of 0.5%^2 (percentage squared), so to correct this lack of sense we calculate standard deviation which gives 7.1% in this example. This last value can be compared with other distribution variances.
I think talking about variance and standard deviation, from a qualitative perspective, is the same since both are dispersion metrics and their objectives are the same (to quantify dispersion, so risk).

 

[fullset]

When people say variance to denote risk, I think they actually mean to say variation.