How can I calculate the "Median" of floating point numbers

I have three two-dimensional arrays containing floating point numbers. I would like to construct a two-dimensional array that contains the "median" or middle value (not the mean) of the three arrays.

For example, if one element of the arrays contained 4.81, 3.54, and 3.56, I'd like to return 3.56, which is the middle value.

How can I do that?

Answer 1

[James Tursa]

E.g.,

x = randi(10,2,3)

x = 2×3

8 4 8 2 8 4

y = randi(10,2,3)

y = 2×3

10 5 5 6 5 8

z = randi(10,2,3)

z = 2×3

9 8 3 4 9 4

xyz = cat(3,x,y,z)

xyz = 
xyz(:,:,1) =

     8     4     8
     2     8     4


xyz(:,:,2) =

    10     5     5
     6     5     8


xyz(:,:,3) =

     9     8     3
     4     9     4

result = median(xyz,3)

result = 2×3

9 5 5 4 8 4

[Jim McIntyre]

Thank you. The problem is that my arrays contain floating point (not integer) data. Median is not defined for floats.

[Jim McIntyre]

So, I guess I could do it this way:

% Create 3 sets of random floats

x = 10*rand(2,3);

y = 10*rand(2,3);

z = 10*rand(2,3);

% concatenate into one array

xyz = cat(3,x,y,z);

% Sort the array by the concatenated dimension

mySort = sort(xyz,3);

% "median" value is the middle dimension of the sorted array

myMedian = mySort(:,:,2);

[Stephen23]

"The problem is that my arrays contain floating point (not integer) data. Median is not defined for floats."

It works for me:

xyz = rand(5,2,3)

xyz = 
xyz(:,:,1) =

    0.8215    0.3983
    0.8312    0.7147
    0.3064    0.6462
    0.2125    0.1865
    0.1640    0.5522


xyz(:,:,2) =

    0.9147    0.3333
    0.6415    0.7983
    0.7675    0.3656
    0.9837    0.5875
    0.7603    0.1577


xyz(:,:,3) =

    0.7413    0.5188
    0.9827    0.6645
    0.8191    0.0133
    0.5869    0.5078
    0.8860    0.0753

out = median(xyz,3)

out = 5×2

0.8215 0.3983 0.8312 0.7147 0.7675 0.3656 0.5869 0.5078 0.7603 0.1577

[James Tursa]

My example used floating point arrays. It works just fine. I generated the "values" in the floating point arrays as integers for clarity of reading, but the arrays x, y, and z are double type. Of course median is defined for floats. Why do you think it isn't? E.g.,

x = 10*rand(2,3)

x = 2×3

0.3831 8.9951 1.2761 7.9274 9.1824 3.5166

y = 10*rand(2,3)

y = 2×3

3.2278 6.2243 2.1488 4.1835 5.4137 4.0934

z = 10*rand(2,3)

z = 2×3

5.5379 8.8700 1.6625 7.5657 4.0267 9.6280

median(cat(3,x,y,z),3)

ans = 2×3

3.2278 8.8700 1.6625 7.5657 5.4137 4.0934

[Jim McIntyre]

Thank you. That answer works.

My original problem was in trying to calculate the median of the arrays without concatenating them. My original code was in the form:

myMedian = median(x(:),y(:),z(:))

[James Tursa]

The concatenation is going to take extra time and memory for the temporary data copies, which will slow performance. Could be avoided with a mex routine, but I wouldn't bother with that unless your variables are huge and the performance hit is significant.