# What is the variance of the following numbers?: {49, 49, 52, 53, 58, 62, 68, 75}

The variance of the given numbers is 1/8((49-58.25)^2+(49-58.25)^2+(52-58.25)^2+(53-58.25)^2+(58-58.25)^2+(62-58.25)^2+(68-58.25)^2+(75-58.25)^2=78.44
Variance is the average squared distance from the mean. Here, the mean of the numbers is $58.25$, so we are taking the distance of each value from the mean and squaring them to get the squared deviations. We then sum up these squared deviations, and divide them by the number of values we have, which is $8$, to get their average.