A measure similar to variance that's always between 0 and 1? Consider the following histogram, obtained from around 1000 measures of distance.

As you can observe, most of the data appears near the mean arond the value 5-10. I also have some isolated samples far away at values 100, 160.
1) Is there any statistical measure I can use to detect when this happens? Sometimes there are no outliers and I'm trying to detect such cases. I was thinking of thresholding variance, but I'm looking for a measure with a value in a fixed interval (e.g. always 0 to 1).
2) I'm trying to get an interval like the one in red that only includes the measures around the mean. I'm looking for a method that works for different histograms with a similar shape (number of readings and values can vary, but shape is always similar). Could you suggest me a method?

One example of such functions is the exponential family:
$$f(v) = \exp[-v^k/s^k]$$
You input variance, which is in $[0,+\infty]$ and you get out something which is $[0,1]$


*

*If variance is $0$ you get $1$ out and 

*the larger variance the closer you will get to $0$.

*$s$ and $k$ are both parameters you can steer how fast to shrink to $0$.


If you want the opposite you can just take $1-f(v)$ instead.
