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?

To answer the title question, if $|X - X_0| \leq 1$, then the variance of $X$ has to be bounded by $1$. So you could use any real-valued function that collapses the range of $X$ down to an interval of radius 1.
For example, you could measure
$$ \mathrm{Var}\left( \frac{2}{\pi} \arctan(X - X_0) \right) $$
(this answer does not attempt to address any of the contents of the post)
