notation for median of function executed for a number of different values.

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Problem



What is the clearest mathematical notation for the following situation:



If I have a function $f(x)$ that is executed for an arbitrary range and step e.g. from $x = 0$ to $x = 10$ with step 2. How do I express the median of all computed values?



What I already have



I had the idea to split the problem into two parts. The first part is representing a set of computed values of $f(x)$ according to the defined limits and step size as $F$. Whereas the second part is simply defining the median as $M$ so that $M(F)$ is the solution to my problem.



But I am unable to write the first step. How should I proceed?




notation




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  • What do you mean from your example? That we are only considering $f(0),f(2),f(4),f(6),f(8),f(10)$?
    – gd1035
    Jul 26 at 19:46










  • Yes, in that example we are only considering $f(0), f(2), f(4), f(6), f(8), f(10)$
    – dll
    Jul 26 at 19:48










  • Could you let $F$ denote the set of values for $f(x)$ with the given step size, in sorted order? Then you can just take the middle value, or the average of the two middle values.
    – gd1035
    Jul 26 at 19:54















up vote
0
down vote

favorite












Problem



What is the clearest mathematical notation for the following situation:



If I have a function $f(x)$ that is executed for an arbitrary range and step e.g. from $x = 0$ to $x = 10$ with step 2. How do I express the median of all computed values?



What I already have



I had the idea to split the problem into two parts. The first part is representing a set of computed values of $f(x)$ according to the defined limits and step size as $F$. Whereas the second part is simply defining the median as $M$ so that $M(F)$ is the solution to my problem.



But I am unable to write the first step. How should I proceed?




notation




share|cite|improve this question



















  • What do you mean from your example? That we are only considering $f(0),f(2),f(4),f(6),f(8),f(10)$?
    – gd1035
    Jul 26 at 19:46










  • Yes, in that example we are only considering $f(0), f(2), f(4), f(6), f(8), f(10)$
    – dll
    Jul 26 at 19:48










  • Could you let $F$ denote the set of values for $f(x)$ with the given step size, in sorted order? Then you can just take the middle value, or the average of the two middle values.
    – gd1035
    Jul 26 at 19:54













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Problem



What is the clearest mathematical notation for the following situation:



If I have a function $f(x)$ that is executed for an arbitrary range and step e.g. from $x = 0$ to $x = 10$ with step 2. How do I express the median of all computed values?



What I already have



I had the idea to split the problem into two parts. The first part is representing a set of computed values of $f(x)$ according to the defined limits and step size as $F$. Whereas the second part is simply defining the median as $M$ so that $M(F)$ is the solution to my problem.



But I am unable to write the first step. How should I proceed?




notation




share|cite|improve this question











Problem



What is the clearest mathematical notation for the following situation:



If I have a function $f(x)$ that is executed for an arbitrary range and step e.g. from $x = 0$ to $x = 10$ with step 2. How do I express the median of all computed values?



What I already have



I had the idea to split the problem into two parts. The first part is representing a set of computed values of $f(x)$ according to the defined limits and step size as $F$. Whereas the second part is simply defining the median as $M$ so that $M(F)$ is the solution to my problem.



But I am unable to write the first step. How should I proceed?





notation





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 26 at 19:32









dll

1157




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  • What do you mean from your example? That we are only considering $f(0),f(2),f(4),f(6),f(8),f(10)$?
    – gd1035
    Jul 26 at 19:46










  • Yes, in that example we are only considering $f(0), f(2), f(4), f(6), f(8), f(10)$
    – dll
    Jul 26 at 19:48










  • Could you let $F$ denote the set of values for $f(x)$ with the given step size, in sorted order? Then you can just take the middle value, or the average of the two middle values.
    – gd1035
    Jul 26 at 19:54

















  • What do you mean from your example? That we are only considering $f(0),f(2),f(4),f(6),f(8),f(10)$?
    – gd1035
    Jul 26 at 19:46










  • Yes, in that example we are only considering $f(0), f(2), f(4), f(6), f(8), f(10)$
    – dll
    Jul 26 at 19:48










  • Could you let $F$ denote the set of values for $f(x)$ with the given step size, in sorted order? Then you can just take the middle value, or the average of the two middle values.
    – gd1035
    Jul 26 at 19:54
















What do you mean from your example? That we are only considering $f(0),f(2),f(4),f(6),f(8),f(10)$?
– gd1035
Jul 26 at 19:46




What do you mean from your example? That we are only considering $f(0),f(2),f(4),f(6),f(8),f(10)$?
– gd1035
Jul 26 at 19:46












Yes, in that example we are only considering $f(0), f(2), f(4), f(6), f(8), f(10)$
– dll
Jul 26 at 19:48




Yes, in that example we are only considering $f(0), f(2), f(4), f(6), f(8), f(10)$
– dll
Jul 26 at 19:48












Could you let $F$ denote the set of values for $f(x)$ with the given step size, in sorted order? Then you can just take the middle value, or the average of the two middle values.
– gd1035
Jul 26 at 19:54





Could you let $F$ denote the set of values for $f(x)$ with the given step size, in sorted order? Then you can just take the middle value, or the average of the two middle values.
– gd1035
Jul 26 at 19:54
















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