I'll still want to see your context, but I'll tell you more about what I see.
First, your formula, as I understand it, is
\(\displaystyle S_n=C*median_i(median_j|x_i−x_j|)\)
What this would mean is that you first take one value of i and find the value of \(\displaystyle |x_i−x_j|\) for each value of j (that is, the absolute difference of your chosen value and every value in the data set (including the one your chose) and find the median of those n values. Repeat this for every value of i, so you will get a list of n medians; take the median of all those. Finally, you multiply by the given value of C.
For your data,
{1,3,5,6}, the work would look like this:i=1: {|1-1|, |1-3|, |1-5|, |1-6|} = {0, 2, 4, 5}, median = 3
i=2: {|3-1|, |3-3|, |3-5|, |3-6|} = {2, 0, 2, 3}, median = 2
i=3: {|5-1|, |5-3|, |5-5|, |5-6|} = {4, 2, 0, 1}, median = 1.5
i=4: {|6-1|, |6-3|, |6-5|, |6-6|} = {5, 3, 1, 0}, median = 2
median of {3, 2, 1.5, 2} = 2
1.1926 * 2 = 2.3852.
But I don't find that formula anywhere other than in your question here and on Stack Exchange. What I do find in various places is Median Absolute Deviation, which is
\(\displaystyle MAD = median( |X\)\(\displaystyle _i − median(X)| )\)
or, as I find it elsewhere looking more like yours, e.g. here,
\(\displaystyle MAD = b median_i( |x_i − \)\(\displaystyle median_j(x_j)| )\)
That would be calculated differently; but the "b" in the latter, which is called "k" in the Wikipedia page, is a constant that depends on the type of distribution, which converts MAD into an approximation of the standard deviation, which would be called s, so this may well be what your formula is supposed to be.
If I calculate the MAD for your example (using your constant), I get this:
median({1, 3, 5, 6}) = 4
median({|1-4|, |3-4|, |5-4|, |6-4|}) = median(3, 1, 1, 2) = 1.5
1.1926 * 1.5 = 1.7889
I'm very curious about what your problem really is about.