[Question]
  [
Given a string of ASCII characters, output the character that is in the middle. If there is no middle character (when the string has an even length), output the ASCII character whose ordinal is the floored average of the two center characters. If the string is empty, an empty string should be output.
Test cases:
```
12345 => 3
Hello => l
Hiya => q
(empty input) => (empty output)
```
Shortest program in characters wins. (Not bytes.)
# Leaderboard
The Stack Snippet at the bottom of this post generates the leaderboard from the answers a) as a list of shortest solution per language and b) as an overall leaderboard.
To make sure that your answer shows up, please start your answer with a headline, using the following Markdown template:
```
## Language Name, N characters 
```
where `N` is the size of your submission. If you improve your score, you *can* keep old scores in the headline, by striking them through. For instance:
```
## Ruby, <s>104</s> <s>101</s> 96 characters 
```
If there you want to include multiple numbers in your header (e.g. because your score is the sum of two files or you want to list interpreter flag penalties separately), make sure that the actual score is the *last* number in the header:
```
## Perl, 43 + 2 (-p flag) = 45 characters 
```
You can also make the language name a link which will then show up in the snippet:
```
## [><>](http://esolangs.org/wiki/Fish), 121 characters 
```
```
<style>body { text-align: left !important} #answer-list { padding: 10px; width: 290px; float: left; } #language-list { padding: 10px; width: 290px; float: left; } table thead { font-weight: bold; } table td { padding: 5px; }</style><script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"> <div id="language-list"> <h2>Shortest Solution by Language</h2> <table class="language-list"> <thead> <tr><td>Language</td><td>User</td><td>Score</td></tr> </thead> <tbody id="languages"> </tbody> </table> </div> <div id="answer-list"> <h2>Leaderboard</h2> <table class="answer-list"> <thead> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr> </thead> <tbody id="answers"> </tbody> </table> </div> <table style="display: none"> <tbody id="answer-template"> <tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr> </tbody> </table> <table style="display: none"> <tbody id="language-template"> <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr> </tbody> </table><script>var QUESTION_ID = 64599; var ANSWER_FILTER = "!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe"; var COMMENT_FILTER = "!)Q2B_A2kjfAiU78X(md6BoYk"; var OVERRIDE_USER = 47556; var answers = [], answers_hash, answer_ids, answer_page = 1, more_answers = true, comment_page; function answersUrl(index) { return "https://api.stackexchange.com/2.2/questions/" + QUESTION_ID + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER; } function commentUrl(index, answers) { return "https://api.stackexchange.com/2.2/answers/" + answers.join(';') + "/comments?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + COMMENT_FILTER; } function getAnswers() { jQuery.ajax({ url: answersUrl(answer_page++), method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { answers.push.apply(answers, data.items); answers_hash = []; answer_ids = []; data.items.forEach(function(a) { a.comments = []; var id = +a.share_link.match(/\d+/); answer_ids.push(id); answers_hash[id] = a; }); if (!data.has_more) more_answers = false; comment_page = 1; getComments(); } }); } function getComments() { jQuery.ajax({ url: commentUrl(comment_page++, answer_ids), method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { data.items.forEach(function(c) { if (c.owner.user_id === OVERRIDE_USER) answers_hash[c.post_id].comments.push(c); }); if (data.has_more) getComments(); else if (more_answers) getAnswers(); else process(); } }); } getAnswers(); var SCORE_REG = /<h\d>\s*([^\n,<]*(?:<(?:[^\n>]*>[^\n<]*<\/[^\n>]*>)[^\n,<]*)*),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*<\/h\d>)/; var OVERRIDE_REG = /^Override\s*header:\s*/i; function getAuthorName(a) { return a.owner.display_name; } function process() { var valid = []; answers.forEach(function(a) { var body = a.body; a.comments.forEach(function(c) { if(OVERRIDE_REG.test(c.body)) body = '<h1>' + c.body.replace(OVERRIDE_REG, '') + '</h1>'; }); var match = body.match(SCORE_REG); if (match) valid.push({ user: getAuthorName(a), size: +match[2], language: match[1], link: a.share_link, }); else console.log(body); }); valid.sort(function (a, b) { var aB = a.size, bB = b.size; return aB - bB }); var languages = {}; var place = 1; var lastSize = null; var lastPlace = 1; valid.forEach(function (a) { if (a.size != lastSize) lastPlace = place; lastSize = a.size; ++place; var answer = jQuery("#answer-template").html(); answer = answer.replace("{{PLACE}}", lastPlace + ".") .replace("{{NAME}}", a.user) .replace("{{LANGUAGE}}", a.language) .replace("{{SIZE}}", a.size) .replace("{{LINK}}", a.link); answer = jQuery(answer); jQuery("#answers").append(answer); var lang = a.language; lang = jQuery('<a>'+lang+'</a>').text(); languages[lang] = languages[lang] || {lang: a.language, lang_raw: lang.toLowerCase(), user: a.user, size: a.size, link: a.link}; }); var langs = []; for (var lang in languages) if (languages.hasOwnProperty(lang)) langs.push(languages[lang]); langs.sort(function (a, b) { if (a.lang_raw > b.lang_raw) return 1; if (a.lang_raw < b.lang_raw) return -1; return 0; }); for (var i = 0; i < langs.length; ++i) { var language = jQuery("#language-template").html(); var lang = langs[i]; language = language.replace("{{LANGUAGE}}", lang.lang) .replace("{{NAME}}", lang.user) .replace("{{SIZE}}", lang.size) .replace("{{LINK}}", lang.link); language = jQuery(language); jQuery("#languages").append(language); } }</script>
```
  
[Answer]
# Pyth, 15 bytes
```
Cs.O@R/lz2_BCMz
```
[Demonstration](https://pyth.herokuapp.com/?code=Cs.O%40R%2Flz2_BCMz&input=Hiya&debug=0)
Starting with "Hiya" as input:
```
              z    "Hiya"                                      Input
            CM     [72, 105, 121, 97]                          Character values
          _B       [[72, 105, 121, 97], [97, 121, 105, 72]]    Pair with reversal
      /lz2         2                                           Halfway index
    @R             [121, 105]                                  That element in each
  .O               113.0                                       Average
 s                 113                                         Floor
C                  "q"                                         Cast to character
                   q                                           Print implicitly
```
Note that this crashes with an error on empty input, and prints nothing to STDOUT, which is a valid way to output an empty string by code-golf defaults.
[Answer]
# Brainf\*\*\*, 61 bytes
# [Chinese](https://esolangs.org/wiki/Chinese), 16 characters
This requires the input is in the ASCII range 1-127 and is null-terminated. It deletes pairs of characters from the start and end of the string until there are one or two characters remaining. If there are two, it adds them together, then divides by 2, rounding down. The remaining character is printed.
```
,[>,]<<<[[<]>[-]>[>]<[-]<<<]>[[->+<]>[-[-<+<]>>]<[>]<[>]<<]>.
```
Try it on [this interpreter](http://brainfuck.tk/).
Dissection:
```
,[>,]         Get the null terminated input
<<<           Move to the second last character
[             While there are at least 3 characters
  [<]>           Move to the first character
  [-]            Delete it
  >[>]<          Move to the last character
  [-]            Delete it
  <<<            Move the the third last character
]
>              Move to the second last character
[              If there are two characters remaining
  [->+<]         Add the two characters together
  >[-[-<+<]>>]   Divide the character by 2 rounding down
  <[>]<[>]<<     Move to before the character to exit the if loop
]
>.             Print the remaining character
```
\* Given each instruction could be compressed to 3 bits and encoded in UTF-32, the whole program could technically be expressed in 6 characters.
**EDIT:** And thanks to [Jan Dvorak](https://codegolf.stackexchange.com/users/7209/jan-dvorak) for introducing me to [Chinese](https://esolangs.org/wiki/Chinese), which compresses this into 16 characters, on par with [Dennis'](https://codegolf.stackexchange.com/users/12012/dennis) [CJam answer](https://codegolf.stackexchange.com/a/64601/4934).
```
ËúêËïàÂ∏ëËÅøÁ∫ÇËÉØÁÆ©ÊÇöË°ÖÈπäÈ¢ÇÈπõÊãÆÊãÆÊ∞∞‰∫∫
```
[Answer]
# CJam, 16 bytes
```
q:i_W%.+_,2/=2/c
```
[Try it online!](http://cjam.tryitonline.net/#code=cTppX1clLitfLDIvPTIvYw&input=aGl5YQ)
### How it works
```
q                e# Read all input.
 :i              e# Cast each character to integer.
   _W%           e# Push a reversed copy.
      .+         e# Perform vectorized addition.
        _,2/     e# Get the length, divided by 2.
            =    e# Select the corresponding sum.
             2/c e# Divide by 2 and cast to character.
```
[Answer]
## Python 3, ~~61~~ ~~59~~ ~~57~~ 55 bytes
I try not to golf with languages I work in, but this isn't too evil.
*Thanks to @xsot for 2 bytes!*
```
lambda x:chr((ord(x[len(x)//2])+ord(x[~len(x)//2]))//2)
```
The full program is 59 bytes:
```
x=input()
l=len(x)//2
print(chr((ord(x[l])+ord(x[~l]))//2))
```
Try it [here](https://repl.it/B2mj/4).
[Answer]
# [TeaScript](https://github.com/vihanb/TeaScript), 23 [bytes](https://en.m.wikipedia.org/wiki/ISO/IEC_8859) ~~25 30 31 33~~
```
¬≤(x[t=xn/2]c+xv[t]c)/2)
```
Uses @isaacg's idea of reversing the string.
[Try it online](http://vihanserver.tk/p/TeaScript/#?code=%22%C2%B2(x%5Bt%3Dxn%2F2%5Dc%2Bxv%5Bt%5Dc)%2F2)%22&inputs=%5B%22hiya%22%5D)
[Test all of the cases](http://vihanserver.tk/p/TeaScript/#?code=%22_m(%23(x%3Dl,%20%20%C2%B2(x%5Bt%3Dxn%2F2%5Dc%2Bxv%5Bt%5Dc)%2F2)%20%20))%22&inputs=%5B%2212345%22,%22Hello%22,%22Hiya%22,%22%22%5D&opts=%7B%22int%22:false,%22ar%22:false,%22debug%22:false,%22chars%22:false,%22html%22:false%7D)
## Ungolfed && Explanation
TeaScript is still JavaScript so it functions a lot like JavaScript too.
```
C((x[t=xn/2]c+xv[t]c)/2)
C((           // Char code to char
   x[t=xn/2]c // Floored center
   +          // Add to
   xv[t]c     // Ceil'd center
  ) / 2)      // Divide by 2
```
[Answer]
# 8086 machine code + DOS, 31 bytes
Hexdump:
```
BA 1E 01 B4 0A CD 21 8B F2 46 8A 1C D0 EB 8A 50
01 72 06 74 08 02 10 D0 EA B4 02 CD 21 C3 FF
```
Assembly source code (can be assembled with tasm):
```
    .MODEL TINY
    .CODE
    org 100h
    MAIN PROC
    mov dx, offset buf
    mov ah, 10      ; DOS function "read string"
    int 21h
    mov si, dx
    inc si          ; si now points to the length of the string
    mov bl, [si]    ; 
    shr bl, 1       ; divide the length by 2
    mov dl, [si+bx+1] ; load the middle char
    jc calc_done    ; if length was odd - done
    jz output_done  ; if length was zero - exit
    add dl, [si+bx] ; add the other middle char
    shr dl, 1       ; divide by 2
calc_done:
    mov ah, 2       ; DOS function "output char"
    int 21h
output_done:
    ret
buf db 255          ; maximum bytes to input
    MAIN ENDP
    END MAIN
```
There is some delicate usage of the FLAGS register here. After it shifts the length of the string right by 1 bit (which is equivalent to division by 2), two flags store additional information:
* Carry flag: contains the bit that was shifted out. If the bit is 1, the length was odd.
* Zero flag: shows whether the result is zero. If the carry flag is 0 and the zero flag is 1, the length was zero, and nothing should be printed.
Normally, the flags should be checked immediately, but here I use the fact that the `mov` instruction doesn't change flags. So they can be examined after loading the middle char.
[Answer]
# Matlab, ~~39~~ 37 bytes
`floor((end+[1,2])/2)` returns the middle two indices of the string if the length is even, and returns the middle indice twice if the length is odd.
`mean` just returns the mean of those values and `char` automatically floors it.
```
@(s)char(mean(s(floor(end/2+[.5,1]))))
```
[Answer]
# [Husk](https://github.com/barbuz/Husk), 11 bytes
```
c¬ΩS¬§+√∂c‚Üí‚Üê¬Ω‚Üî
```
[Try it online!](https://tio.run/##ASQA2/9odXNr//9jwr1TwqQrw7Zj4oaS4oaQwr3ihpT///8iSGl5YSI "Husk ‚Äì Try It Online")
# Explanation
Delicious, delicious combinators all the way down. `√∂` is "compose these four functions", `¬§` is "apply the first argument to the results of applying the second argument to two additional arguments separately", `S` is "apply this function (which should take two arguments) to `S`'s third argument and to the result of applying `S`'s second argument to its third". Therefore,
```
   Function       Type                Semantics
     √∂c‚Üí‚Üê¬Ω        [TChar]->TInt       ASCII code of middle (floored) char in string
   ¬§+√∂c‚Üí‚Üê¬Ω        [TC]->[TC]->TI      Sum of ASCII codes of middle of two strings
  S¬§+√∂c‚Üí‚Üê¬Ω‚Üî       [TC]->TI            Sum of ASCII codes of the middle of a string and its reverse
c¬ΩS¬§+√∂c‚Üí‚Üê¬Ω‚Üî       [TC]->TC            ASCII character represented by half the above, QEF
```
Edited to add:
Strictly speaking, this fails slightly to conform to the problem specification, which requests a string in the case of an empty input and a character in other cases.
Due to Husk's strict typing, it's just not possible to define a function/program that can return either of two types. I chose to return a single character in all cases, and for Husk, the most reasonable choice for a single character to represent the empty string is `'(space)'` because that's the "default" value (and in fact, that's why this program returns it; the default value is used when taking the last (`‚Üí`) item of an empty list).
I could have also reasonably chosen to return strings of zero or one characters, which would fail the specification in the other direction, but I didn't because it adds four bytes: `·π†&√∂;c¬ΩS¬§+√∂c‚Üí‚Üê¬Ω‚Üî`, with the `;` converting the character to a one-character string, another `√∂` to explicitly compose the needful, and a `·π†&` to shortcut in the case of falsy input.
[Answer]
# Prolog, 111 bytes
**Code**
```
p(X):-atom_codes(X,L),length(L,N),I is N//2,J is(N-1)//2,nth0(I,L,A),nth0(J,L,B),Q is(A+B)//2,writef('%n',[Q]).
```
**Explained**
```
p(X):-atom_codes(X,L),       % Convert to list of charcodes
      length(L,N),           % Get length of list
      I is N//2,             % Get mid index of list
      J is(N-1)//2,          % Get 2nd mid index of list if even length
      nth0(I,L,A),           % Get element at mid index
      nth0(J,L,B),           % Get element at 2nd mid index
      Q is(A+B)//2,          % Get average of elements at mid indices
      writef('%n',[Q]).      % Print as character
```
**Examples**
```
>p('Hello').
l
>p('Hiya').
q
```
[Answer]
# [R](https://www.r-project.org/), 73 bytes
```
function(x,y=utf8ToInt(x),n=sum(1|y))if(n)intToUtf8(mean(y[n/2+c(1,.5)]))
```
[Try it online!](https://tio.run/##K/qfpmCj@z@tNC@5JDM/T6NCp9K2tCTNIiTfM69Eo0JTJ8@2uDRXw7CmUlMzM00jTzMzryQkPxSoQiM3NTFPozI6T99IO1nDUEfPVDNWU/N/moaSoZGxiamSJheQ6ZGak5MPZWZWJkJYmZVIktiIzEqcUhCdSpr/AQ "R ‚Äì Try It Online")
Many thanks to @ngm for coming up with this non-recursive idea - allowed to golf 20 bytes.
Old solution:
### [R](https://www.r-project.org/), ~~101~~ 95 bytes
```
"!"=function(x,n=sum(1|x))"if"(n<3,mean(x),!x[-c(1,n)])
try(intToUtf8(!utf8ToInt(scan(,""))),T)
```
[Try it online!](https://tio.run/##DcoxCsMwDEbhPbewJv2gDCFLhuYA3d2pdCgmBg@WIZHBhdzd9fKW7529k6M9Vg2WinIT3a@aebkbQCkS62OVfHwHQVx7z4EXUXww2fnjpObLy@LGro768lTjK4xbiACIRyfqfw "R ‚Äì Try It Online")
Recursive solution. Corrected one issue at the price of 2 bytes:
* added `try(expr, silent = TRUE)` to properly manage the case where the input is empty.
thanks Giusppe for 4 bytes !
[Answer]
# C++14, 56 bytes
```
[](auto s){int l=s.size();return(s[(l-1)/2]+s[l/2])/2;};
```
Anonymous lambda taking string as an argument and returning int as char code. For `""`, it returns `0`. Not sure how exactly the input and output should look like (is not specified in the question).
Ungolfed, with usage
```
#include <string>
int main()
{
    auto lmbd = [](auto str)
    {
        int len = str.size();
        return (str[(len - 1) / 2] + str[len / 2]) / 2;
    };
    std::cout << (char) lmbd("Hiya"s) << std::endl; // outputs q
}
```
[Answer]
# JavaScript (ES6), 83 bytes ~~89 91~~
*Saved 2 bytes thanks to @C·¥è…¥·¥è Ä O'B Ä…™·¥á…¥*
*Saved 6 bytes thanks to @ETHproductions*
```
s=>String.fromCharCode((s[~~(t=s.length/2-.5)][q='charCodeAt']()+s[0|t+.9][q]())/2)
```
JavaScript's not too good at all this string char code.
[Answer]
# [O](https://github.com/phase/o), ~~44~~ 34 bytes
[Crossed out 44 is still regular 44 :(](https://codegolf.stackexchange.com/a/63373)
```
ise.eJ;2/m[(\($L;dJ{#\#+2/c}L;?o];
```
Bytes wasted on:
* Checking if the input's length is even/odd
* Getting the middle character(s)
[Answer]
## [Minkolang 0.13](https://github.com/elendiastarman/Minkolang), ~~23~~ 20 bytes
```
$oI2$%d$z,-Xz3&+2:O.
```
[Try it here.](http://play.starmaninnovations.com/minkolang/?code=%24oI2%24%25d3%7EG%2C-X3%26%2B2%3AO%2E%0A%24oI2%24%25d%24z%2C-Xz3%26%2B2%3AO.&input=hiya)
### Explanation
```
$o        Read in the whole stack as characters
I2$%      Push I,2, then pop them and push I//2,I%2
d$z       Duplicate top of stack (I%2) and store in register (z)
,-X       <not> the top of stack, subtract, and dump that many off the top of stack
z3&       Retrieve value from register and jump 3 spaces if this is not zero
   +2:    Add and then divide by 2
O.        Output as character and stop.
```
[Answer]
# [Japt](https://github.com/ETHproductions/Japt), ~~40~~ ~~29~~ ~~23~~ ~~21~~ 20 bytes
*Saved 4 bytes thanks to @◊ün…üu…ê…Ø…π…ê◊üo…Ø*
Now only half the original length! I love code golf. :-D
```
UcV=K*Ul)+Uw cV)/2 d
```
Works properly on the empty string. [Try it online!](https://codegolf.stackexchange.com/a/62685/42545)
### How it works
```
          // Implicit: U = input string, K = 0.5
Uc        // Take the char-code at position
 V=K*Ul   //  V = 0.5 * length of U
+         //  (auto-floored), plus
Uw cV     //  the char-code at position V (auto-floored) in the reversed string,
/2 d      //  divide by 2, and turn back into a character (auto-floored).
          // Implicit: output last expression
```
As you can see, it uses a lot of auto-flooring. (Thanks, JavaScript!) Suggestions welcome!
[Answer]
# Go, ~~166~~ ~~156~~ 153 bytes
Go may not be the best language for golfing... but I love it, so so much, and I'm learning it, so there.
This implementation accepts blank (`\n`) input and **will probably break with non-ASCII/ASCII-extended input.** However, OP has not specified input/output encoding thus ASCII is all I've explicitly supported.
*Edit*: turns out `if`/`else` *is* shorter than `switch`. Now I know, I suppose.
Golfed:
```
package main;import ."fmt";func main(){a:="";_,_=Scanln(&a);if b:=len(a);b>0{x:=b/2;if b%2==0{Printf("%c",(a[x]+a[x+1])/2)}else{Println(string(a[x]))}}}
```
Ungolfed:
```
package main # everything in go is a package.
import . "fmt" # the dot allows for absolute package method references 
# (think "from string import *" in python)
func main() {
    a := ""
    _, _ = Scanln(&a) # a pointer to a
    if b := len(a); b > 0 { # if statements allow local assignment statements
        x := b / 2
        if b%2 == 0 { # modulo 2 is the easiest way to test evenness
#in which case, average the charcodes and print the result
            Printf("%c", (a[x]+a[x+1])/2)
        } else {
# else just find the middle character (no rounding needed; integer division in Go always results in an integer)
            Println(string(a[x]))
        }
    }
}
```
[Answer]
# ùîºùïäùïÑùïöùïü, 23 chars
```
a=√ØÍùà/2,œöƒé((√Ø√ºa+·¥ô√Ø√ºa)/2)
```
`[Try it here (Firefox only).](http://molarmanful.github.io/ESMin/interpreter.html?eval=false&input=asdf&code=a%3D%C3%AF%EA%9D%88%2F2%2C%CF%9A%C4%8E%28%28%C3%AF%C3%BCa%2B%E1%B4%99%C3%AF%C3%BCa%29%2F2%29)`
Thanks to @ETHProductions for the idea!
[Answer]
# C#, 77 bytes
```
s=>{int n=s.Length;return n<1?' ':(char)(n%2>0?s[n/2]:(s[n/2-1]+s[n/2])/2);};
```
It doesn't actually return a string, and you'll get a space character if the input string is empty because the function must always return a value. 2 more bytes would be needed to return a string.
Full program with test cases:
```
using System;
namespace FindTheCenter
{
    class Program
    {
        static void Main(string[] args)
        {
            Func<string,char>f= s=>{int n=s.Length;return n<1?' ':(char)(n%2>0?s[n/2]:(s[n/2-1]+s[n/2])/2);};   //77 bytes
            Console.WriteLine(f(""));
            Console.WriteLine(f("Hello"));
            Console.WriteLine(f("Hiya"));
        }
    }
}
```
---
Alternatively, a full program which reads user input and prints the center of the entered string:
# C#, 144 bytes
```
using C=System.Console;class P{static void Main(){var s=C.ReadLine();int n=s.Length;C.Write(n<1?' ':(char)(n%2>0?s[n/2]:(s[n/2-1]+s[n/2])/2));}}
```
Again, it uses the same trick of printing a space character, which the user will not notice, and not an empty string, otherwise the solution is 2 bytes longer.
[Answer]
## Vim, ~~38~~ ~~24~~ 23 keystrokes
Because vim has a built in function to find the middle *line* but not the middle *char*, we split every character on a separate line first using `substitute`, find the middle line, then delete everything after and before it. 
```
:s/\./\0\r/g<cr>ddMjdGkdgg
```
If you want to run this, beware of `.vimrc` files which may change the behavior of `.` (magic regex) and `g` (gdefault). Note that it actually saves me 3 keystrokes on my machine :)
## Previous answer
```
:exe 'norm '.(virtcol('$')/2).'|d^ld$'
```
Takes a one line buffer as input, updates the current buffer with the middle character. I thought there would have been a shortcut for this in vim! 
Note: a potentially shorter solution seems to cause an infinite loop... If someone has an idea: `qq^x$x@qq@qp` (12 keystrokes) - it works with `<c-c>` after the last `@q`...
[Answer]
# Excel, ~~122~~ 79 bytes
Actually @Sophia Lechner's answer now:
```
=IFERROR(CHAR(CODE(MID(A8,LEN(A8)/2+.5,1))/2+CODE(MID(A8,LEN(A8)/2+1,1))/2),"")
```
---
-5 bytes from initial solution thanks to @Taylor Scott.
```
=IFERROR(IF(ISODD(LEN(A1)),MID(A1,LEN(A1)/2+1,1),CHAR((CODE(MID(A1,LEN(A1)/2,1))+CODE(MID(A1,LEN(A1)/2+1,1)))/2)),"")
```
12 bytes needed for Empty String.
[Answer]
# Haskell, 87 bytes
A nice recursive solution is possible here:
```
import Data.Char
f[]=[]
f[c]=[c]
f[c,d]=[chr(ord c+div(ord d-ord c)2)]
f(c:s)=f$init s
```
[Answer]
# [Jelly](https://github.com/DennisMitchell/jelly), 7 bytes
```
J√Ü·πÅ·ªã¬π√Üm
```
[Try it online!](https://tio.run/##y0rNyan8/9/rcNvDnY0Pd3cf2nm4Lff/0ckPdy5@1DBHwdZO4VHD3Ic7FvnrHG5Xebi7JwshyvVw95bD7Y@a1kT@/29oZGxiChI35vIAmpgPYuZweWRWJoJYhQA "Jelly ‚Äì Try It Online")
Takes input as a list of codepoints. Outputs a single codepoint.
## How it works
```
J√Ü·πÅ·ªã¬π√Üm - Main link. Takes a string S on the left
J       - Indices of S
 √Ü·πÅ     - Median
    ¬π   - Yield S
   ·ªã    - Index into S
     √Üm - Get their arithmetic mean
```
The `√Ü·πÅ` median atom returns the mean of the two central elements if the list has an even list. When the list is the indices of `S` (i.e. `[1, 2, ..., len(S)]`), this will always be half the sum of an odd and an even integer, so the result will be \$x + \frac 1 2, x \in \mathbb N\$.
When indexing with non-integers such as \$x + \frac 1 2\$, Jelly instead uses the pair \$[x, x+1]\$ to index, which, in this case, results the two central characters if the list length is even.
[Answer]
# [Vyxal](https://github.com/Lyxal/Vyxal) `K`, 8 bytes
```
‚Ä°·∏¢·π™‚Üî·π™t·πÅ‚åä
```
[Try it Online!](http://lyxal.pythonanywhere.com?flags=K&code=%E2%80%A1%E1%B8%A2%E1%B9%AA%E2%86%94%E1%B9%AAt%E1%B9%81%E2%8C%8A&inputs=%2212345%22&header=&footer=)
Explanation:
```
          # 'K' flag - Strings are inputted as a list of ordinal values
‚Ä°·∏¢·π™‚Üî      # Remove the first and last elements elements of the list until empty, returning intermittent values
    ·π™t    # Remove all but the second to last element of the list
      ·πÅ   # Take the average of the middle character(s)
       ‚åä  # Floor
          # 'K' flag - Output numbers as characters
```
[Answer]
# Mathematica, ~~118~~ 99 chars
```
Floor
If[#=="","",FromCharacterCode[%@Mean@#[[Ceiling[l=Length@#/2];;%[l+1]]]&@ToCharacterCode@#]]&
```
Mma character code manipulation is *pricey*...
[Answer]
#  VBA, 130 Bytes
```
Function a(q)
h=Len(q):a=Mid(q,(h)/2,2)
If h Mod 2=0 Then:a=Chr((Asc(Left(a,1))+Asc(Right(a,1)))\2):Else:a=Right(a,1)
End Function
```
> 
> Finds the Middle 2 Characters.   
> 
>  If number of Characters is Odd then get the Right of the Middle 2 which will be the true middle as we rounded down.   
> 
>  If not sum the ASCII `asc()` values of the 2 Characters divided by 2 and return the ASCII Character `chr()` based on that value.
> 
> 
> 
I think I can golf away one of the `asc()` calls, but couldn't get it to work shorter. 
[Answer]
# K, 40 bytes
```
{(*|r;`c$_(+/r:2#l_x)%2)@l=_l:-1+(#x)%2}
```
[Answer]
## ><>, 24 + 3 (for -s) = 27 bytes
```
l1+l4(*9$.~{~
;
o;
+2,o;
```
Old solution (Doesn't work for empty input):
```
l3(?v~{~
?vo;>l2=
;>+2,o
```
Both take input on the stack through `-s`. Both are 24 bytes.
[Try it online here.](http://fishlanguage.com/playground)
[Answer]
# [pb](https://esolangs.org/wiki/pb), 83 bytes
```
^<b[1]>>>w[B!0]{<w[B!0]{t[B]<b[T]>>}<b[0]<b[0]<[X]>>}w[B=0]{<}t[B]<[X]t[B+T]vb[T/2]
```
While there are at least 3 characters in the input string, the first and last are removed. This leaves either 1 character (should be printed unmodified) or 2 (should be averaged and printed). To handle this, the first and last characters of the string are added together and divided by two. If there was only one character, `(a+a)/2==a`. If there was two, `(a+b)/2` is the character that needs to be printed. pb "borrows" Python's expression evaluation (`def expression(e): return eval(e, globals())`) so this is automatically floored.
Handling empty input costs me 5 bytes. Specifically, `<b[1]>` on the first line. Earlier, when I said "string", that was a total lie. pb doesn't have strings, it has characters that happen to be close to each other. Looking for the "last character of a string" just means moving the brush to the left until it hits a character. When no input is provided, the "while there are at least 3 characters" loop is skipped entirely and it starts looking for the last character. Without that `<b[1]>`, it would keep looking forever. That code puts a character with a value of 1 at (-1, -1) specifically to be found when the input is empty. After finding the "last character" of the string the brush assumes the first one is at (0, -1) and goes there directly, finding a value of 0. `(1+0)/2` is 0 in pb, so it prints a null character.
> 
> But monorail, that's still printing! The challenge specification says `(empty input) => (empty output)`! Isn't printing a null character cheating? Also, this is unrelated, but you are smart and handsome.
> 
> 
> 
Thanks, hypothetical question-asker. Earlier, when I said "print", that was a total lie. In pb, you don't really print values, you just place them on the canvas. Rather than "a way to output", it's more accurate to imagine the canvas as an infinitely large 2D array. It allows negative indices in either dimension, and a lot of programming in pb is really about making sure the brush gets to the location on the canvas that you want it. When the program finishes executing, anything on the canvas with non-negative X and Y coordinates is printed to the appropriate location on the console. When the program begins, the entire canvas is filled with values of 0. In order to not have to print an infinite number of lines, each with an infinite number of null bytes, each line of output is only printed up to the last nonzero character, and lines are only printed up to the last one with a nonzero character in it. So putting a `0` at (0, 0) is still an empty output.
**Ungolfed:**
```
^<b[1]>                # Prevent an infinite loop on empty input
>>w[B!0]{              # While there are at least 3 chars of input:
    <w[B!0]{              # Starting at the second character:
            t[B]<b[T]>>         # Copy all characters one position to the left
                                # (Effectively erasing the first character)
    }
    <b[0]<b[0]            # Delete both copies of the last character
    <[X]>>                # Get in place to restart loop
}
w[B=0]{<}                 # Go to last character of remaining string
t[B]<[X]t[B+T]            # Find it plus the first character
vb[T/2]                   # Divide by 2 and print
```
[Answer]
## CoffeeScript, ~~104~~ 103 bytes
```
f=(x)->((y=x.length)%2&&x[y//2]||y&&String.fromCharCode (x[y/=2][z='charCodeAt']()+x[y-1][z] 0)//2)||''
```
[Answer]
# Ruby, ~~43~~ ~~42~~ 41 bytes
```
->a{s=a.size;puts s<1?'':s%2<1??q:a[s/2]}
```
**42 bytes**
```
->a{s=a.size;puts s==0?'':s%2<1??q:a[s/2]}
```
**43 bytes**
```
->a{s=a.size;puts s==0?'':s%2<1?'q':a[s/2]}
```
**Usage:**
```
->a{s=a.size;puts s<1?'':s%2<1??q:a[s/2]}['12345']
=> 3
```
]