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Given a list of numbers, is it possible to find out (or in other words, is there a statistical measure to tells the) the closeness of the numbers (do note that i am not talking about correlation - this would be for 2 sequences - something like correlation between height and weight).

I am looking for something like a closeness coefficient for a given series of numbers, so given a series [0,10,20,30,40] - the 'closeness coefficient' gives me the spread of the numbers.

It would also be nice if the 'closeness coefficient' depicts the 'density' of the numbers - but if this is a different computable statistical measure, then it shouldnt be a problem.

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  • $\begingroup$ It would be useful to know more about the scale these values come from - is the data continuous or categorical? Are differences meaningful, or are the measurements just ordinal? A dispersion measure for, e.g., unordered categorical needs to be different from such a measure for continous interval data. $\endgroup$ – caracal Dec 27 '10 at 14:29
  • $\begingroup$ The simplest possible one is the range: 40 - 0 = 40. The mean density of the numbers can be estimated as the quantity divided by the range; e.g., 5/40 = 1/8 (one value for every difference of eight). $\endgroup$ – whuber Dec 28 '10 at 0:41
  • $\begingroup$ How is Mean Density of Numbers and Quartiles different? I mean, statistically, dont you think quartiles convey this information in a better way? $\endgroup$ – venkasub Dec 29 '10 at 4:15
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The simplest would be the standard deviation. Other measures of 'scale' include the MAD (median absolute deviation), the IQR (interquartile range), Winsorized standard deviation, etc. You might also be interested in the Index of Disperson, the Coefficient of Variation, or other measures of 'dispersion'.

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I'd use standard deviation, like shabbychef said. See http://en.wikipedia.org/wiki/Variance to learn more.

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