# How to calculate theoretical quantiles of an odd dataset?

In order to calculate a set of theoretical quantiles I usually apply the following method:

$\frac{1}{2. N} + \frac{x}{N}$

so here this makes:

$\frac{1}{24} + \frac{6}{12}$

$\frac{1}{24} + \frac{7}{12}$

$\frac{1}{24} + \frac{8}{12}$

etc... untill I get $\frac{1}{24} + \frac{11}{12}$

And I can just look up every result in a table I am given.

Knowing these results I can also use those same results to get the negative values (confer image). $\frac{1}{24} + \frac{11}{12}$ = 0.958 => 1,73(which I found in my table) becomes -1,73, etc...

In other words I'll do 6 aditions and get there negatives -> 12 values

Now What if I have a dataset of 13 datapoints? Because if I would apply the rule I just explained. I'd either do 7 additions resulting in 14 theoretical quantiles