       How Functions are Applied to Matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg66064] How Functions are Applied to Matrices
• From: Gregory Lypny <gregory.lypny at videotron.ca>
• Date: Fri, 28 Apr 2006 06:32:58 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello everyone,

If I use functions, such as Mean, StandardDeviation, or Total, that
operate on lists, they work the way I expect when applied to a single
list.  So, for example, the mean of data[] below is 5.25.
However, when I apply Mean to the entire 3 x 4 matrix, which I
understand to be three lists, I expect to get three means.  Instead I
get four because Mean is operating on the columns and not the rows,
that is, the four corresponding elements of each of the three lists.

Why is that?

Greg

data={{-9,8,3,1},{2,12,3,4},{-6,-9,-9,8}}

The mean of the second list:

In:=
Mean[data[]]//N

Out=
5.25

Applying Mean to the whole matrix computes the mean of columns, not
rows.

In:=
Mean[data]//N

Out=
{-4.33333,3.66667,-1.,4.33333}

I need to Map it to have it applied to each list.

In:=
Map[Mean,data]//N

Out=
{0.75,5.25,-4.}

```

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