An Elegant Variation

An Elegant Variation

A statistician makes use of a concept called the Variance. It is used to measure the extent that a set of given values deviate from the average of all the values in a distribution, such as test scores. As a simplified example, take the values represented by the numbers 1,2,3. The standard approach to calculating the Variance is to add the three values and divide by 3, yielding an average of 2 which is called the Mean; then subtracting the Mean from each of the three values yields –1, 0, and +1. These are then squared, resulting in +1, 0, and +1, or a sum of 2, which when divided by the number of elements (3), produces a net result of 2/3 or .667. This is the Variance for this particular distribution, which signifies how far each number deviates from the Mean.

Uncle Garabed, with his penchant for word play, has recast the method in a formula that reads: The Variance = The Mean of the Square minus The Square of the Mean.

It goes like this:

The Mean of the Square

1 squared = 1

2 squared = 4

3 squared = 9

Total 14 divided by 3 = 4.667

The Square of the Mean

1 + 2 + 3 = 6 divided by 3 = 2 (Mean)

2 squared = 4

Net = .667 (Variance)