Measures of Variation

Measures of Variation - Stats: Measures of Variation Range...

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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 corresponding parameter. This formula has the problem that the estimated value isn't the same as the
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Measures of Variation - Stats: Measures of Variation Range...

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