How would you find the variance in this problem?

Question

1. Scores on an exam: 65, 62, 83, 80, 78

please show some work so i can understand instead of just copying the answers

Answer 1

Another method. Less clever math, but easier to remember.
First find the mean. It is (65+62+83+80+78)/5=73.6
Now you construct a new series of differences from the mean by subtracting the mean from each member, and you get -8.6,-11.6,9.4,6.4,4.4
Now you sum the squares of the new series and divide the result by N (5 in this case). You get 71.44

Answer 2

The variance of a sample is given by ∑x²/n - (∑x/n)². So, finding the square of the mean and the mean of the squares:

∑x/n = (65+62+83+80+78)/5 = 73.6
∑x²/n = (65²+62²+83²+80²+78²)/5 = 5488.4

Variance = 5488.4 - 73.6² = 71.44