Variance vs. variation

keep_running · December 16, 2016, 4:02am

What is the difference between variance and variation of varibles in a regression model?

tickersu · December 16, 2016, 8:31am

Variance is a parameter of a distribution (standard deviation squared) that helps us describe the distribution’s shape and the data spread. Variation is a less precise term intended to describe changes in the values of a variable or the spread of data.

keep_running · December 17, 2016, 4:45am

Sorry, I am confused. Can you provide an example?

Thank you!

Iampossible · December 17, 2016, 7:17am

Variance is the average of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean.

Sample 1: 100, 101, 103, 105, 136,140 => sample standard deviation = 18.5

Sample 2: 3, 12, 35,105,153, 205 => sample standard deviation = 82.4

So the sample standard deviation (and hence the sample variance, since variance is standard deviation squared) for sample 2 is greater than sample 1.

We can easily see that the observations are more “dispersed” from the mean for sample 2, compared to sample 1.

Now variation is a more generic term used to describe the dispersion/spread of the data from the mean. It doesn’t have a single precise formula.

You can view variance as a measure of variation. You can also view standard deviation as a measure of variation. We could even calculate spread = largest value - smallest value as a measure of variation.

Frankliving · December 30, 2016, 10:51am

Wonderful explanation!!!

Iampossible:

Variance is the average of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean.

Sample 1: 100, 101, 103, 105, 136,140 => sample standard deviation = 18.5

Sample 2: 3, 12, 35,105,153, 205 => sample standard deviation = 82.4

So the sample standard deviation (and hence the sample variance, since variance is standard deviation squared) for sample 2 is greater than sample 1.

We can easily see that the observations are more “dispersed” from the mean for sample 2, compared to sample 1.

Now variation is a more generic term used to describe the dispersion/spread of the data from the mean. It doesn’t have a single precise formula.

You can view variance as a measure of variation. You can also view standard deviation as a measure of variation. We could even calculate spread = largest value - smallest value as a measure of variation.