How to find the Mean of results given as a list of Rules?

Question

How can we find the mean of the following type of data?

{{β -> 0.516819}, {β -> 0.499907}, 
 {β -> 0.494064}, {β -> 0.472742}, 
 {β -> 0.537485}, {β -> 0.478291}, 
 {β -> 0.523855}, {β -> 0.483624}, 
 {β -> 0.50126},  {β -> 0.527267}}

Which command could be used to find the mean of this data?

Welcome to SE! It will help those might answer if you would please post code that is syntactically correct and properly formatted. See editing help. — Michael E2, Jan 23 '14 at 12:49
This should be helpful: Using the result of Solve in subsequent calculations, together with Mean. — Michael E2, Jan 23 '14 at 12:51
@JacobAkkerboom Sorry, it was involuntary. Please rollback my edit to yours if think it better. (or merge both!) — Dr. belisarius, Jan 23 '14 at 13:08

score 5 · Answer 1 · answered Jan 23 '14 at 12:53

5

Mean[beta /. {{beta -> 0.516819}, {beta -> 0.499907}, {beta -> 
     0.494064}, {beta -> 0.472742}, {beta -> 0.537485}, {beta -> 
     0.478291}, {beta -> 0.523855}, {beta -> 0.483624}, {beta -> 
     0.50126}, {beta -> 0.527267}}]

answered Jan 23 '14 at 12:53

ciao

25,774
2
58
139

score 3 · Answer 2 · edited Jan 23 '14 at 22:19

3

[Beta] is bad syntax, so i replaced all by beta

Mean[{{beta->0.516819},{beta->0.499907},{beta->0.494064},{beta->0.472742},
{beta->0.537485},{beta->0.478291},{beta->0.523855},{beta->0.483624},{beta->0.50126},
{beta->0.527267}}[[All,1,2]]]

If you want the variance, try opening the documentation and search for it

edited Jan 23 '14 at 22:19

Szabolcs

234,956
30
623
1,263

answered Jan 23 '14 at 12:44

Coolwater

20,257
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Jacob Akkerboom · Answer 3 · 2014-01-23T22:18:11.880

Considering the votes, I think Timings are in order.

Double semicolons are intentional, they prevent extra memory use when $HistoryLength > 1

Timing comparison between other answers

nn = 1*^6;
rands = RandomReal[1, nn]; ;
data = {b -> #} & /@ rands; ;

Mean@data[[All, 1, 2]] // Timing
Mean@(b /. data) // Timing

Outputs

{0.069164, 0.500199}
{0.983088, 0.500199}

Perhaps also noteworthy

<<Developer`
data[[All, 1, 2]] // PackedArrayQ
(b /. data) // PackedArrayQ

Outputs

False
False

How to find the Mean of results given as a list of Rules?

3 Answers3