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The wiki excerpt of the tag reads:

An algorithm is a a set of one or more computations that will produce a calculated result. All statistics methods are algorithms. Algorithms can be simple, such as calculating a percentage, or can be very complex and require a computer for fast and accurate results.

I am not an expert, but this strikes me as off. To me an algorithm is a recipe - a set of instructions for doing something. Usually it means a very precise set of instructions.

And I think "all statistics methods are algorithms" is misleading. It's true that you can reduce any particular statistical technique to an algorithm (you have to do that for computers) but ... we do some things with our brains that aren't that! Isn't deciding on which method to use a "method"?

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    $\begingroup$ Is your question just the question at the end ("Isn't deciding on which method to use a "method"?") or is the intended question something broader? $\endgroup$ – Glen_b♦ Nov 1 '17 at 23:53
  • $\begingroup$ I'm also not sure of "computations". I'd use "instructions". $\endgroup$ – Peter Flom♦ Nov 2 '17 at 0:09
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    $\begingroup$ More important is that many models or methods can be implemented in different ways, and each implementation would correspond to a different algorithm. $\endgroup$ – kjetil b halvorsen Nov 3 '17 at 15:56
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This is a bad wiki excerpt; it is imprecise and too lengthy (see What is the optimal length & level of detail of tag wiki excerpts?)

Wikipedia defines algorithm as "an unambiguous specification of how to solve a class of problems". This sounds good to me. I would replace the wiki excerpt by

An unambiguous specification of how to solve a class of problems [Wikipedia]

I think it's fine to copy a definition from elsewhere, in particular for the non-statistical terms. (For statistical terms, it often does make sense to write a wiki excerpt that is tailored for our site.)

Update: Based on the discussion in the comments, here is my preferred version based on @Scortchi's wording:

An unambiguous list of computational steps involved in finding a solution to a class of problems.

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    $\begingroup$ (We can also replace "specification" by "set of instructions" as suggested by @Peter. $\endgroup$ – amoeba Nov 2 '17 at 9:33
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    $\begingroup$ As well as saying what an algorithm is, we should think about what we want people to use the tag for. To me it suggests an emphasis on the computional steps involved in finding a solution rather on specifying a solution. $\endgroup$ – Scortchi♦ Nov 2 '17 at 10:18
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    $\begingroup$ Related: stats.meta.stackexchange.com/questions/3146 $\endgroup$ – amoeba Nov 2 '17 at 10:18
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    $\begingroup$ @Scortchi I agree but I am not sure this requires any further additions to the excerpt. Or do you mean we should write "An unambiguous set of computational steps involved in finding a solution to a class of problems"? I like this too. $\endgroup$ – amoeba Nov 2 '17 at 10:22
  • $\begingroup$ I do like that version more, but I was trying to think what might give clear, pithy usage guidance. The algorithms tag seems unnecessary in a fair few of the posts to which it's been attached. $\endgroup$ – Scortchi♦ Nov 2 '17 at 11:27
  • $\begingroup$ So, should I make this change? $\endgroup$ – Peter Flom♦ Nov 2 '17 at 12:29
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    $\begingroup$ @Peter, yes, I'd say go ahead. My favourite formulation at the moment is "An unambiguous list of computational steps involved in finding a solution to a class of problems" (which is based on Scortchi's wording; compared to the previous comment I replaced "set" with "list" because it's ordered :-) $\endgroup$ – amoeba Nov 2 '17 at 12:44

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