suppose you calculate a mean of a population and you want to know how representative that mean is of a random?

Question

data point in that population. In other words, is the data bunched tightly around the mean, or is it more loosely distributed over the possible range of values?

Answer 1

What you're looking for is the standard deviation. If the data values are X and the mean is XBAR, then

S.D. = sqrt{[SUM(X - XBAR)^2] / n}

n is the number of data items, and SUM means to add up the squares of the differences between the data values and the mean.

The lower the standard deviation, the more tightly packed the data. If the data is normally distributed, about 68% of the data will lie within one standard deviation of the mean, and 95% will be within two standard deviations.

[Edit: In light of the previous answers, I should add that the standard deviation is the square root of the variance.]

Answer 2

What you need is called "variance". Variance is a measure of statistical dispersion. A small number will mean "data bunched tightly" and a large number will tell you "loosely distributed over the possible range of values".
Wikipedia article referenced below will show you how to calculate it -- it would not be fair for me to try to cram all that in this little text box.

Answer 3

That's what the variance is for.