What does sumd method in k-means clustering function exactly calculate?

I am doing basic experiments with kmeans function. As a real simple example, say that I have a data set of 4 items with 1 attribute and this attribute is their value:

Data=[1;2;3;4];

If I want to split this data set into 2 clusters I should get one centroid in 1.5 and another in 3.5:

[idx,C,sumd]=kmeans(Data,2)

C =     
1.5000
3.5000

and I get it. However to my understanding sumd in this case should be:

abs(1-1.5)+abs(2-1.5) or  abs(3-3.5)+abs(4-3.5)

ans =

       1

but I am getting sumd as:

sumd =

      0.5000
      0.5000

for both clusters. Instead of getting 1's for both.

My question is what exactly does sumd calculate?

Answer 1

[Ameer Hamza]

If you look at the documentation of kmeans(), you will know that it uses the square of the Euclidean distance, by default. So you should calculate it like this

abs(1-1.5).^2+abs(2-1.5).^2 or  abs(3-3.5).^2+abs(4-3.5).^2

ans = 
  0.5 (both cases)

[Onur Kapucu]

Thanks

Answer 2

[the cyclist]

It's because the default distance metric used is the squared Euclidean distance (for minimization, and reporting). See the Distance input parameter.

[Onur Kapucu]

Thanks