Stats: Measures of Variation
Range
The range is the simplest measure of variation to find. It is simply the highest value
minus the lowest value.
RANGE = MAXIMUM - MINIMUM
Since the range only uses the largest and smallest values, it is greatly affected by
extreme values, that is - it is not resistant to change.
Variance
"Average Deviation"
The range only involves the smallest and largest numbers, and it would be desirable to
have a statistic which involved all of the data values.
The first attempt one might make at this is something they might call the average
deviation from the mean and define it as:
The problem is that this summation is always zero. So, the average deviation will
always be zero. That is why the average deviation is never used.
Population Variance
So, to keep it from being zero, the deviation from the mean is squared and called the
"squared deviation from the mean". This "average squared deviation from the mean"
is called the variance.
Unbiased Estimate of the Population Variance
One would expect the sample variance to simply be the population variance with the
population mean replaced by the sample mean. However, one of the major uses of