# Probability and Variance

Discussion in 'Mathematics' started by kalowski, Mar 28, 2011.

1. pg 127 from MEI Statistics 1 textbook: "The most useful measure of central tendency is the mean or expectation...and the most useful measure of spread is the variance."

Why the variance and not the standard deviation? Anyone know? Am I stupid?

3. I think that they are referring to the Variance/SD being more useful than Range or IQR.

I have often wondered why we have the two different terms for what is actually the same measure.

Why not have V and root V?

Or SD and SD^2?

4. Hmmm I don't. I think they are suggesting that the variance is preferable to the sd. The sd can be used to calulate outliers, hasd teh same units as the data and is good for comparing distrbutions. The variance is good for ....

And that MEI newsletter is the one about the divsor of n or n-1 where the MEI introduced all that terminology, root mean square deviation, etc, whcih was different to what everyone and every exam board was teaching!

5. I agree - I like much of the MEI stuff but I also think they just "get their knickers in a twist" now and again in the need to be "technically correct"

I think here they are refering to the fact that variance can generally be applied to random variables and has apllications in regression/correlation rather than being a better measure of spread of a distribution

6. I'm not sure what the problem is here. If one is talking about population variance and population standardard deviation then they are simply related, so provide the same amount of information.
The real difference comes when we come to to samples from a population. Then for the unbiased estimate of the variance we have the n -> n-1 thing. Unfortunately, for the unbiased estimate of the standard deviation we cannot simply take the square root of the unbiased estimate of the sample variance. The fact is that they are not equal.

7. 'Do they? For a frequency distribution I can make good use of mean plus 2 or 3 standard deviaions, the variance doesn't give me a similar measure (well, it does... but I have to calculate the sd!)'
I still don't understand the problem. To calculate the standard deviation one has to work out the variance and then take its square root. You can then do what you like with it.
A probability distribution can be obtained from a frequency distribution - this changes neither the variance nor the standard deviation, nor the uses of the latter.
Variance is considered more important than standard deviation by statisticians because of its nice mathematical properties with respect to combining independent random variables and particularly in the context of the normal distribution.