You could use regular reference lines to create these, but Tableau doesn't allow you to create reference lines on a typical histogram (one that uses Bins), so I'd suggest that you create a calculated field which calculates your bins. You can then use that to create a regular bar chart, which will allow for reference lines. To do that, follow these steps:
1) Create a parameter called Bin Size so that the bin size is configurable.
2) Create a calculated field called LC Bin with the following formula: INT([LC to Opportunity Create Date]/[Bin Size])*[Bin Size]
3) Drag LC Bin to the columns shelf in place of the existing bin dimension.
4) Drag Bin Size to the Size card, then set the size to "Fixed".
At this point, you should have a histogram that looks exactly like your original.
5) Create a calculated field called Mean that calculates your mean (i.e. average): {FIXED : AVG([LC to Opportunity Create Date])}
6) Add all your filters to context so they are calculated before the LOD above is calculated.
7) Drag Mean to detail, then create a reference line on it, like this:
It should now look like this:
8) Follow similar steps to create a band or distribution reference line for your standard deviation.
FYI. I learned most of this from the following so please take a look at them as well
Discussion: Reference line over a distribution graph
Post by Jonathan Drummey: histograms | Drawing with Numbers
