How to calculate variance?

If your textbook is not clear on these matters, I highly recommend Gravetter and Walnau's "http://www.amazon.com/exec/obidos/ASIN/0495602205/metafilter-20/ref=nosim/". I taught myself out of it. Old editions are just as good as new ones.

http://en.wikipedia.org/wiki/Analysis_of_varianceis where I think you might start.

Just take the second moment of the distribution. ∫[(x-c)^2]f(x) dx where c is the mean and f(x) is the probability density function.

Thank you, ptm. But I think it was much simpler than that page makes it. Is variance just the sum of the data points, less the mean, squared, and divided by two? And based on that how do I calculate the between-groups variance and total variance? To others: I appreciate the suggestion to start with my textbook or class notes, as I never could have thought of that on my own. There is no textbook for the course, and my notes for this day of class are less than sufficient.

The variance is the mean of the squares of (i - M), where the "i"s are the data values and M is the mean of all data points. If your data are 9, 10, 11, then the mean is 10; the squares of (i-M) are 1, 0, and 1; the variance is (1+0+1)/3 = 0.66 If your data are 5, 10, and 15, then the mean is still 10; the squares of (i-M) are 25, 0, and 25; the variance is (25 + 0 + 25) /3 = 16 I assume that you're getting "2" from some example, but that number should be either N or N-1. Can't help you with why it's sometimes N-1 rather than N.

What I should have said in the first place is that if you were one of my students, I'd much rather you came to me with questions. Between-groups variance is conceptually the same thing as within-group variance, but it's handled on the group means rather than the individual values. So let's say you had the groups 9, 10, 11; 4, 5, 6; and 18, 20, 22. The first group has the mean of 10. The second group has a mean of 5. The third group has a mean of 20. The Grand Mean of these is 11.66 The between-groups variance is the sum of n_i * ( (mean_i - Grand_mean) ^2 ). so in this example, it's [3 * (1.66)^2 ] + [3 * 6.66^2] + [3 * 8.33^2]. Try this page: http://people.richland.edu/james/lecture/m170/ch13-1wy.html or this page: http://www.sjsu.edu/faculty/gerstman/StatPrimer/anova-a.pdf Where I am likely to have led you astray is the difference between using N or N-1 to divide by. I am no stats god; this is meant as a starting point and not an ending point. I am likely to have gotten something kind of wrong, but maybe it will feel less mysterious.

Although this is probably too late for you, the magic search term is http://www.uwsp.edu/psych/stat/12/anova-1w.htm or one-way classification. People didn't directly answer your question because answering homework questions is contrary to the guidelines. There are several good reasons for that.