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 statistics is to estimate the
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 Spring '07
 Bagwhandee
 Standard Deviation, Mean, data values, average deviation

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