What is variability of a set of numerical data?

Answer 1

Variability is determined by the how numbers are distributed across the set of numbers. There are several ways of measuring this the most common is standard deviation. To find standard deviation you first find the average of the set by adding them all up and dividing by the amount of numbers in the set. Then you find the square of each number in the set minus the average. You add all these values up, multiply them by 1/the number of items in the set, and take the square root. As an example the set {2,5,3,6} has much less variability as measured by the standard deviation than {2000,-1000,-500,484} even though they both have the same average. The firsts average is (2+5+3+6)/4 or 4. The standard deviation is

the square root of(((2-4)^2+(5-4)^2+(3-4)^2+(6-4)^2)*1/4) or about

1.58113883. The standard deviation of the second set that has the same average as the first is the square root of (((2000-4)^2+(-1000-4)^2+(-500-4)^2+(484-4)^2)*1/4) or 1170.09059.