To calculate the variance of a given set of numbers, you follow these steps:
Find the mean (average) of the numbers. Mean = (3+1+2+4) / 4 = 2.5
Subtract the mean from each number and square the result. (3-2.5)^2 = 0.25 (1-2.5)^2 = 2.25 (2-2.5)^2 = 0.25 (4-2.5)^2 = 2.25
Find the sum of all the squared differences. 0.25 + 2.25 + 0.25 + 2.25 = 5
Divide the sum by the total number of numbers (in this case, 4). Variance = 5 / 4 = 1.25
Therefore, the variance of the given set of numbers 3, 1, 2, and 4 is 1.25.
