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Dispersion (Measures of)

Dispersion (Measures of):

Measures of dispersion express quantitatively the degree of variation or dispersion of values in a population or in a sample . Along with measures of central tendency , measures of dispersion are widely used in practice as descriptive statistics . Some measures of dispersion are the standard deviation , the average deviation , the range , the interquartile range .

For example, the dispersion in the sample of 5 values (98,99,100,101,102) is smaller than the dispersion in the sample (80,90,100,110,120), although both samples have the same central location – "100", as measured by, say, the mean or the median . Most measures of dispersion would be 10 times greater for the second sample than for the first one (although the values themselves may be different for different measures of dispersion).

It is important from a practical standpoint that measures of dispersion are normally constructed to be shift invariant and scale invariant . If a measure is not scale invariant, for example, then the value of dispersion might depend on the units of measurement. For example, say the value of dispersion of prices of a particular CD-player model across a country is $10. If the measure of dispersion is scale-invariant and you convert all the prices from dollars to cents by multiplying them by 100, then the measure of dispersion will change from 10 (dollars) to 1000 (cents).

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