Re: How Functions are Applied to Matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg66096] Re: [mg66064] How Functions are Applied to Matrices*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sat, 29 Apr 2006 03:40:52 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

m=Array[a,{3,4}]; Mean takes each row of the array as a single element of the outer list to be averaged. Mean[m]==(m[[1]]+m[[2]]+m[[3]])/3 True Bob Hanlon ---- Gregory Lypny <gregory.lypny at videotron.ca> wrote: > 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[[2]] 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[182]:= > Mean[data[[2]]]//N > > Out[182]= > 5.25 > > Applying Mean to the whole matrix computes the mean of columns, not > rows. > > In[181]:= > Mean[data]//N > > Out[181]= > {-4.33333,3.66667,-1.,4.33333} > > I need to Map it to have it applied to each list. > > In[183]:= > Map[Mean,data]//N > > Out[183]= > {0.75,5.25,-4.} >