Hypothetical question about dispersion I have two series, A and B.
If the range of A is greater than the range of B and the interquartile of A is smaller than that of B, which series is more dispersed ?
 A: There is no one measure of how much a variable is "dispersed". Instead there are many, some of them being range, interquantile range, standard deviation, mean absolute deviation, Gini's mean difference...
Each statistics is different and measures the same thing from a different angle, so they all show different nuances of the same phenomenon. If you start to use some of them, you can learn to make sense of their different behaviour and understand what they tell us. Compare their values when looking to the histogram of your variable.
For the sake of writing a report, usual statistics to be presented are min-max, quartiles, mean and st. deviation.
A: It is impossible to say without having a better idea of what kind of dispersion is interesting to the problem.
(Assume zero medians in the following examples.)
The one with a wide range might be clustered very tight to the median with the occasional extreme point (say a zillion), while the other might be fairly normally distributed with a standard deviation of only a few hundred-thousand, meaning that the “mainstream” is spread over a range of maybe a million or so, but a point like a zillion isn’t going to be present.
“Dispersion” then comes down to a subjective judgment, as it doesn’t have the exact mathematical formula that, say, standard deviation has.
A: I usually choose a measure of dispersion that suits the data. If your data are normal and lack "large" outliers (i.e. greater than Cook's Distance), the old-fashioned standard deviation from the mean might be your most robust option. If no clear-cut distribution is evident, I favor the distribution-free Gini's Mean Difference. In R, this would be:
#===============================================================================
# Gini's Mean Difference
#===============================================================================

# x: numeric vector
gini.MD <- function(x) {
  x.order <- sort(x)
  n <- length(x)
  index <- 1:n
  sum.x <- sum((2 * index - n - 1) * x.order)
  g <- (2 / (n^2 - n)) * sum.x
  g
}

Further reading about Gini's Mean Difference:
Yitzhaki, S. (2003). Gini's mean difference: A superior measure of variability for non-normal distributions. International Journal of Statistics, 61(2), 285-316.
Gerstenberger, C., & Vogel, D. (2015). On the efficiency of Gini's mean difference. Statistical Methods and Applications, 24(4).
