Stats: Added a standard function mean to compute arithmetic average

[supreet11agrawal]

Till now, mean in Sympy could be found using E(expectation).
Keeping end users in mind, added a function mean which essentially
does the same thing but can be more easy to understand for new users.

References to other Issues or PRs

Brief description of what is fixed or changed

Other comments

I am not sure about the change in init.py https://github.com/supreet11agrawal/sympy/blob/7561a336c4923e0dfcac8c11475c9efd5acaf52e/sympy/stats/__init__.py#L20
This can be removed as well. This is added here to show functioning

Release Notes

• stats
  • Added a standard function mean for computing arithmetic average

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• stats
  • Added a standard function mean for computing arithmetic average (#16314 by @supreet11agrawal)

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Till now, mean in Sympy could be found using `E`(expectation).
Keeping end users in mind, added a function `mean` which essentially
does the same thing but can be more easy to understand for new users.

<!-- Your title above should be a short description of what
was changed. Do not include the issue number in the title. -->

#### References to other Issues or PRs
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#### Brief description of what is fixed or changed


#### Other comments
I am not sure about the change in `init.py` https://github.com/supreet11agrawal/sympy/blob/7561a336c4923e0dfcac8c11475c9efd5acaf52e/sympy/stats/__init__.py#L20
This can be removed as well. This is added here to show functioning

#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
* stats
  * Added a standard function `mean` for computing arithmetic average
<!-- END RELEASE NOTES -->

[codecov]

Codecov Report

Merging #16314 into master will increase coverage by 0.015%.
The diff coverage is 100%.

@@              Coverage Diff              @@
##            master    #16314       +/-   ##
=============================================
+ Coverage   73.257%   73.272%   +0.015%     
=============================================
  Files          618       618               
  Lines       158200    158201        +1     
  Branches     37175     37175               
=============================================
+ Hits        115893    115918       +25     
+ Misses       36783     36761       -22     
+ Partials      5524      5522        -2

[smichr]

I would merge this with the E(X+y) as

E(X + Y)  # or mean(X + Y), the expected average of two die

[supreet11agrawal]

Yes, this can be done. But a specific example should also be present, I think

[supreet11agrawal]

Tell me if it is better this way

[oscarbenjamin]

There are other things that we might want use the name mean for in future e.g. somthing analogous to np.mean. It doesn't seem very useful to use the name for something redundant like this.

[supreet11agrawal]

There are other things that we might want use the name mean for in future e.g. somthing analogous to np.mean. It doesn't seem very useful to use the name for something redundant like this.

Hmm.., maybe mean will be more useful in that case. But I think a function similar to this must be present in stats. 'Mean', the word itself is quite important in statistics field.

[supreet11agrawal]

Maybe we can have some difference like Mean and mean. Can be confusing though

[oscarbenjamin]

There already is E for expectation which is the standard name for this sort of thing. "Mean" isn't normally used in an algebraic context. Functions called mean are widely used when working with data though i.e. for the sample mean.

[supreet11agrawal]

Functions called mean are widely used when working with data though i.e. for the sample mean.

I agree with you. Although, don't you think that 'data' processing should be part of stats module as well? In that case, mean would have the same purpose. For general data, we can say that it is uniformly distributed and can thus calculate its mean.
I am not sure though.

[smichr]

I think I, too, am leaning towards not making this change in favor of "preferably one way" and (as @oscarbenjamin points out) "expectation" is the standard word in this context. A note in the docstring about what E is might be helpful: "E - the expectation (mean) value of the distribution" or words to that effect.

[oscargus]

I had a similar feeling and strictly it looks like it is OK to use mean for expectation value, but as noted, it is maybe more common to use mean for average value of a series of samples (now, there is an alternative word to use for mean, average, although I guess most people would expect mean to be the average value of samples as in e.g. Matlab). On the other hand, one can easily check the argument to determine if it is samples or a distribution.

With that said: feel free to write a function that computes the average value of a list (or Matrix in a given dimension). It may be useful for certain situations I guess, even from a symbolic perspective.

[supreet11agrawal]

So, I will close this PR. We can add the change in the docs in another PR.

[oscargus]

Naturally, this mean function can return the expectation value if the input is not a list but a distribution. But it would make sense to primarily use it for computing the average of a list/matrix(iterable?).

[supreet11agrawal]

I'll wait for 24Hrs if anyone has to say anything.

[oscarbenjamin]

I think mean of an array makes sense but not mean of a matrix.

[supreet11agrawal]

Yes, we can add that. But where would this function go?

[supreet11agrawal]

@oscarbenjamin It might make sense if we implement it dimension wise. For eg. one may find mean of all the rows. (The result will be a list in that case)

[supreet11agrawal]

See this. Might be of some help in this case
https://www.mathworks.com/help/matlab/ref/mean.html

[asmeurer]

Although, don't you think that 'data' processing should be part of stats module as well?

This tends to be out of scope for SymPy. Generally data is purely numeric, in which case a library like scipy.stats is much better. SymPy should focus on symbolic manipulations. See also #14261.

[supreet11agrawal]

Ok then I think we can close this