I'm given a table

-1 0 1 .31 .38 .31

the question is asking me to find mean of X, variance of X, and standard deviation of X. The answers are

mean = 0

variance = .62

standard deviation = .787

I've been in class everyday and don't think the teach even went over this... I'm looking through the text book in chapter we are studying and found formulas which aren't giving me the correct answers...

I'm not even exactly sure how to get the mean. originally I tried adding up the probabilities (.31 + .38 + .31)/3 = .33 but that wasn't correct. I was supposed to do that for -1, 0, 1...

from my understanding the variance is supposed to be

sum of "value x prob" = -.31 + 0 + .31 = 0 but the answer is .62... why? I've done variance before with that formula, but it's different this time?

I've tried standard deviation using the .62 variance given to me. (-1 - .62)^2 x (.31) + (0 - .62)^2 x (.38) + (1 - .62)^2 x (.31) ...it doesn't = .787 and I've tried experimenting a few different possibilities and still can't reach that number.

I'm lost...