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#C++14, 340 383 bytes

As generic unnamed lambda. First parameter L is the list as std::list of floating point type and second parameter is the desired output stream, like std::cout.

#import<cmath>
#define F(x);O<<x<<'\n';
#define Y l=k;++l!=L.end();
#define A auto
[](A L,A&O){A S=L;A l=L.begin(),k=l;A n=L.size();A s=*l,p=s,d=s*s,h=n/2.;for(S.sort(),Y s+=*l,p*=*l,d+=*l**l);for(l=S.begin();--h>0;++l)F(s)F(p)F(s/n)F(*l)for(Y)O<<*l-*k++<<","F(' ')for(A x:S)O<<x<<","F(' ')F(S.front())F(S.back())F(sqrt((d-s*s/n)/(n-1)))}

Compiles with a warning, C++ does not allow " directly followed by literals like F. Program still running.

• -1 & -2 bytes thanks to Zacharý

Ungolfed:

#include<iostream>
#include<list>

#import<cmath>
#define F(x);O<<x<<'\n';
#define Y l=k;++l!=L.end();
#define A auto

auto f=
[](A L, A&O){
  A S=L;                  //copy the list for later sorting
  A l=L.begin(),          //main iterator
    k=l;                  //sidekick iterator
  A n=L.size();
  A s=*l,                 //sum, init with head of list
    p=s,                  //product, same
    d=s*s,                //standard deviation, formula see https://en.wikipedia.org/wiki/Algebraic_formula_for_the_variance
    h=n/2.;               //for the median later   
  for(
    S.sort(),             //now min/med/max is at known positions in S
    Y //l=k;++l!=L.end(); //skip the headitem-loop
    s += *l,              //l points the next element which is fine
    p *= *l,              //since the head given at definiten
    d += *l * *l          //needs the sum of the squares
  );
  for(
    l=S.begin();          //std::list has no random access
    --h>0;                //that's why single increment loop
    ++l                   //until median is crossed
  )
  F(s)  //O<<s<<'\n';     //sum
  F(p)                    //product
  F(s/n)                  //average
  F(*l)                   //median (in S)
  for(Y) //l=k;++l!=L.end(); //set l back to L
    O<<*l-*k++<<","       //calc difference on the fly
  F(' ')
  for(A x:S)              //output sorted list
    O<<x<<"," 
  F(' ')
  F(S.front())            //minimum
  F(S.back())             //maximum
  F(sqrt((d-s*s/n)/(n-1))) //standard deviation
}

;


using namespace std;

int main() {
 list<double> l = {10,3,1,2,4};
 f(l, cout);
}