Normally distributed data?

1. The problem statement, all variables and given/known data
Suppose I have a set of measurements of a quantity Q, where the resolution R is the same for all data di. However, R is unknown, and I wish to find it.

In my book they do this by writing the likelihood L (or rather, ln(L)) as the Gaussian, so

$$\ln L = \sum\limits_i { - \ln R_i \sqrt {2\pi } } - \sum\limits_i {\frac{{\left( {d_i - Q } \right)^2 }}{{2R_i }}}$$

Now they differentiate wrt. the mean Q and the deviation Ri = R, yielding two equations. Solving these yields

$$R^2 = \frac{1}{N}\sum\limits_i {\left( {d_i - Q} \right)^2 }$$

This is the standard result we are "used" to. But does this mean that every single time I use this formula on a set of data, then I am implicitly assuming that the data is normally distributed?

Cheers.
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