Saturday, September 20, 2014

Variability

Variability (as name inspires) show how much values/elements are different/diverse from each others. When all values are very close to the mean value, it means we have little variability or diversity.

The common used variability measure is the variance (or standard deviation, which is the positive square root of variance). Besides, the range measure can indicate the amount of variability within a group of data.


I guess the formula to compute variability is known, but let's show it again:


Suppose we had the following measurements data {5.2, 5.3, 4.95, 5.17, 5.22}.
The diversity/variability within values seems small by inspection. Calculating the variance s^2=0.01717 which is clearly a small value.

But let's see this group of data {30, 45, 39, 28, 42}.
The diversity/variability within values seems large by inspectionCalculating the variance s^2=55.7 which is clearly a large value.

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