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

enter image description here


For a distribution that's symmetric about zero (you seem to be dealing with a normal, but you should state that explicitly in your question), the middle quantile will be zero.

That one won't have a "partner" of the opposite sign.


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