Does anyone know how to find variability in math!?

Let us use one shoe brand and four months of sales to illustrate the procedure.

Suppose you sold 0, 6, 1 and 3 pairs of Converse shoes

in the first four months of 2008.

Two ways of measuring "variability" would be

1) calculating the difference between the largest and the smallest numbers (which would be easy with the answer of

6 - 0 = 6 here) and

2) calculating the variance of the numbers (which would require knowing two formulas in statistics)

Assuming you want 2) above:

Let E(x) denote the expected value of a set of numbers and

let Var(x) denote the variance of a set of numbers.

With these four numbers, the expected value (or average or mean) is E(x) = (0 + 1 + 3 + 6) / 4 = 2.5.

(Add them up and divide by the total number of numbers.)

And their variance is Var(x) =

[ (0 - 2.5)^2 + (1 - 2.5)^2 + (3 - 2.5)^2 + (6 - 2.5)^2 ] / 4 =

[ (- 2.5)^2 + (- 1.5)^2 + (0.5)^2 + (3.5)^2 ] / 4 =

[ 6.25 + 2.25 + 0.25 + 12.25 ] / 4 = 21 / 4 = 5.25.

(Find the difference between each number and E(x), square all the differences, add them up and divide by the total number of numbers.)

Note: If we didn't square the differences (turning them all into positive numbers), we would always end up with zero (wiping out that information). Taking the square root of Var(x) brings it back down to a number that we can compare with and use with E(x) and that square root value is called the "standard deviation" (often written by hand with the small greek letter sigma or typed STD).

Variability In Math

The ability to change