Computing a mean of median list of points

Question

Given a array of lists with the same number of here N = 10 elements:

SuperList = {{5., 4.99667, 4.99335, 4.99002, 4.98669, 4.98337, 4.98004, 4.97671, 4.97338, 4.97006}, {5., 4.99667, 4.99335, 4.99002, 4.98669, 4.98337, 4.98004, 4.97671, 4.97338, 4.97006}, {5., 4.99667, 4.99335, 4.99002, 4.98669, 4.98337, 4.98004, 4.97671, 4.97338, 4.97006}, {5.,4.99667, 4.99335, 4.99002, 4.98669, 4.98337, 4.98004, 4.97671, 4.97338, 4.97006}, {5.1, 5.09667, 5.09335, 5.09002, 5.08669, 5.08337, 5.08004, 5.07671, 5.07338, 5.07006}, {5., 5., 5., 5., 5., 5., 5., 5., 5., 5.}, {5., 5., 5., 5., 5., 5., 5., 5., 5., 5.}, {5., 5., 5., 5., 5., 5., 5., 5., 5., 5.}, {5., 5., 5., 5., 5., 5., 5., 5., 5., 5.}, {5., 4.99667, 4.99335, 4.99002, 4.98669, 4.98337, 4.98004, 4.97671, 4.97338, 4.97006}};

How do I efficiently compute an array, which we'll call "MedianList" of length N where each element in the array is the median or mean of the sublist entries at the same index in the "SuperList"? For example, the first element would be:

MedianList[[1]] = Median[{5., 5., 5., 5., 5.1, 5., 5., 5., 5., 5.}];

The second element would be:

MedianList[[2]] = Median[{4.99667, 4.99667, 4.99667, 4.99667, 5.09667, 5., 5., 5., 5., 4.99667}];

And so forth.

Answer 1

Doesn't Median[SuperList] do just that?

From the documentation:

${\text{Median}}\left(\left\{\left\{x_1,y_1,\ldots \right\},\left\{x_2,y_2,\ldots \right\},\ldots \right\}\right) \text{ gives } \left\{\text{Median}\left[\left\{x_1,x_2,\ldots \right\}\right],\text{Median}\left[\left\{y_1,y_2,\ldots \right\}\right]\right\} \text{. }$