Calculate Cumulative Mean and Standard Deviation of a list without FOR loops [duplicate]

Question

I have a simple list mylist={x_1,x_2,...,x_N};.

Now I want to map a function over this list, e.g. the Mean and StandardDeviation functions, so that it will give me a list that looks like this:

f/@mylist = {f[{x_1}], f[{x_1, x_2}], f[{x_1, x_2, x_3}], ... , f[{x_1,x_2,...,x_N}]}

How can I achieve that? I know that I can use a simple loop to do so but I am wondering if Mathematica has a specific function for this kind of mapping.

Thanks a bunch!

Answer 1

Turning my comment into an answer:

ClearAll[MapAccumulate];

MapAccumulate[f_, list_List] := f@Take[list, #] & /@ Range@Length@list;

Now you can do stuff like this:

MapAccumulate[Mean, mylist]

Answer 2

Aye carumbah - new versions

lis = {x1, x2, x3, x4};

• Sol1:

FoldList[Append, {}, lis] // Rest

{{x1}, {x1, x2}, {x1, x2, x3}, {x1, x2, x3, x4}}

• Sol2:

sol = FoldList[Join, lis]  /. Join->List

{x1, {x1, x2}, {x1, x2, x3}, {x1, x2, x3, x4}}

One can then Map any desired function, e.g.

Map[Mean, sol]

Above work for numerical versions too.

Earlier Suggestion

My earlier suggestion (see comments from Kuba below) was:

Accumulate[lis] /. Plus -> List

... but that has some behavioural problems with numerical input.