Standard deviation of all matrix elements (single value)

I have a random matrix X and I am looking for the standard deviation considering all elements; however I am asked (by a text book, learning Matlab) not to use loops. The result should be one single value.

std(X) gives a matrix of standard deviation of all columns which is not what I am looking for. (something corresponding to m=mean(mean(X)) it is not working for the standard deviation)

PS: sorry for asking this simple question; I did some search on this topic but couldn't find useful hints.

Thank you for your help!

Answer 1

[Adam]

std( X(:) )

should give you the standard deviation of all elements in a matrix, X, of any shape.

This is also generally better for mean since it works for any dimensionality rather than mean( mean( X ) ) which is hard-coded as 2d.

[Adam]

Please add a comment to an answer rather than a new answer (it is a mistake many make though, not just you!).

The syntax

X(:)

simply collapses your array into a column so that the std command (or any other similar command) will produce a single answer as it would on a normal column array. For statistics where the 2d or n-d structure of the data is irrelevant this works well. Obviously it needs more manipulation for functions where the 2d structure matters.

Answer 2

[Torsten]

Use "reshape" to get an (N*M,1) column vector from the (N,M)-matrix.

Best wishes

Torsten.

Answer 3

[Joachim Schmid]

Thank you very much Torsten and Adam! Adam, now I have to understand the command.