# Measure of closeness

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.

• 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. – caracal Dec 27 '10 at 14:29
• 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). – whuber Dec 28 '10 at 0:41
• How is Mean Density of Numbers and Quartiles different? I mean, statistically, dont you think quartiles convey this information in a better way? – venkasub Dec 29 '10 at 4:15