Finally I have noticed that something is wrong with Mathematica 10.2 version. For example with Mathematica 9.0 the execution is right.

My Mathematica does not hang (Mavericks with 10.2.0) but the computation takes ~18 seconds roughly...

Perhaps your numbers are too small. If I rescale them I get no errors:

Hamerdif = 10^17*{-7.75205766163486/10^17, -5.629097590588154/10^17, 
         -7.30880056733321/10^18, 8.376594318634389/10^17, 
    7.959982479649063/10^18, 
         -5.850425470324006/10^17, -7.563430648620345/10^17, 
    8.99610086221389/10^17, 
         8.047050888271066/10^17, 4.95873023031791/10^17}; 
Sigma = StandardDeviation[Hamerdif];
ir1 = Histogram[Hamerdif, {Sigma/2^6}, "PDF"]

I send you my values again. I think it is better to probe with the same "InputForm" values, Hamerdif = {-7.75205766163486^-17, -5.629097590588154^-17, -7.30880056733321^-18, 8.376594318634389^-17, 7.959982479649063^-18, -5.850425470324006^-17, -7.563430648620345^-17, 8.99610086221389^-17, 8.047050888271066^-17, 4.95873023031791^-17}; Sigma = StandardDeviation[Hamerdif]; ir1 = Histogram[Hamerdif, {Sigma/2^6}, "PDF"]

What is Hamerdif? If it is a list of numbers I get no errors:

Hamerdif = {1, 2, 3, 4, 5};
Sigma = StandardDeviation[Hamerdif];
ir1 = Histogram[Hamerdif, {Sigma/2^6}, "PDF"]

It's difficult to say without the data, but:

1. The square brackets in the binspec should be deleted. In Mathematica they are for function arguments.
2. The binspec calls for bin sizes of 1/2000000 * the standard deviation, which seems crowded.
3. It is best to begin user symbol names with lower case to avoid conflict with reserved names, which Mathematica begins in upper case.

Best, David