Java 7, 152 bytes

String c(String s){char[]a=s.toCharArray();int l=a.length,x,y;return l<2?s:""+(l%2>0?a[l/2]:(char)((x=a[l/2])>(y=a[(l/2)-1])?y+((x-y)/2):x+((y-x)/2)));}

Ungolfed & test cases:

Try it here.

class M{
 static String c(String s){
 char[] a = s.toCharArray();
 int l = a.length,
 x,
 y;
 return l < 2
 ? s
 : "" + (l%2 > 0
 ? a[l/2]
 : (char)((x = a[l/2]) > (y = a[(l/2)-1])
 ? y + ((x-y)/2)
 : x + ((y-x)/2)));
 }
 public static void main(String[] a){
 System.out.println(c("12345"));
 System.out.println(c("Hello"));
 System.out.println(c("Hiya"));
 System.out.println(c(""));
 System.out.println(c("x")); // Additional test case that will fail on some other answers
 }
}

Output:

3
l
q
(empty output)
x

PHP, (削除) 147 (削除ここまで) 93 bytes

Credits and special thanks to Jörg Hülsermann for golfing my answer 54 bytes down!

<?=($l=strlen($s=$argv[1]))%2?$s[($l-1)/2]:chr(floor((ord($s‌​[$l/2])+ord($s[$l/2-‌​1]))/2));

Previous version:

$s=$argv[1];$l=strlen($s);echo($l%2!=0?substr($s,$n=($l-1)/2,-$n):chr(floor(abs((ord($x=substr($s,$l/2-1,1))-ord(substr($s,$l/2,1)))/2))+ord($x)));

Testing code:

$argv[1] = 'Hiya';
$s=$argv[1];
$l=strlen($s);
echo($l%2!=0?substr($s,$n=($l-1)/2,-$n):chr(floor(abs((ord($x=substr($s,$l/2-1,1))-ord(substr($s,$l/2,1)))/2))+ord($x))); 

Test online

(削除) I have the feeling that this can be improved, but not enough time for it... (削除ここまで)

• \$\begingroup\$ <?=($l=strlen($s=$argv[1]))%2?$s[($l-1)/2]:chr(floor((ord($s[$l/2])+ord($s[$l/2-1]))/2)); is my proposal \$\endgroup\$

  Jörg Hülsermann

  – Jörg Hülsermann

  2016年09月27日 23:10:42 +00:00

  Commented Sep 27, 2016 at 23:10
• \$\begingroup\$ @JörgHülsermann Brilliant golfing! You should post it as your own answer. If I have time I will golf my answer more with your nice solutions. Thanks. \$\endgroup\$

  Mario

  – Mario

  2016年09月28日 14:17:04 +00:00

  Commented Sep 28, 2016 at 14:17
• \$\begingroup\$ Feel free to take it as your answer \$\endgroup\$

  Jörg Hülsermann

  – Jörg Hülsermann

  2016年09月28日 14:23:46 +00:00

  Commented Sep 28, 2016 at 14:23

Perl 5, 43 + 5 (-plF'' flag) = 48 bytes

$_&&=chr((ord($F[$==@F/2])+ord$F[-++$=])/2)

Try it online!

Seriously, (削除) 22 (削除ここまで) 20 bytes

,O3 >WXXaXa3 >WXkæ≈c

Thanks @Mego for being great at your language

Try it online or whatever

• 1
  \$\begingroup\$ This fails for empty input. I have a deleted 20-byte solution which I'm also trying to fix for empty input. \$\endgroup\$

  lirtosiast

  – lirtosiast

  2015年11月24日 05:25:25 +00:00

  Commented Nov 24, 2015 at 5:25
• \$\begingroup\$ ,;``@(lIƒ will leave you with the input value on the stack if its len is > 0, or terminate the program otherwise. Note that there's an unprintable in the backticks - character 127. \$\endgroup\$

  user45941

  – user45941

  2015年11月24日 15:46:39 +00:00

  Commented Nov 24, 2015 at 15:46
• \$\begingroup\$ @Mego This doesn't seem to be working. \$\endgroup\$

  jado

  – jado

  2015年11月24日 19:36:50 +00:00

  Commented Nov 24, 2015 at 19:36
• \$\begingroup\$ @phase You gotta quote strings for input. This works. \$\endgroup\$

  user45941

  – user45941

  2015年11月24日 19:42:28 +00:00

  Commented Nov 24, 2015 at 19:42
• \$\begingroup\$ @Mego What is the ƒ supposed to do? \$\endgroup\$

  jado

  – jado

  2015年11月24日 19:56:02 +00:00

  Commented Nov 24, 2015 at 19:56

Excel VBA, (削除) ₁₀₁ (削除ここまで) 81 bytes

Immediate window function that takes input from cell [A1] and outputs to the VBE immediate window

l=[Len(A1)]/2:s=[A1]&" ":If l Then?Chr((Asc(Mid(s,l+.5))+Asc(Mid(s,l+1)))2円)Else?

Lua, 128 bytes

p=...i=math.ceil(#p/2)s=string b=s.byte a=p:sub(i,i)io.write(#p==0 and""or#p/2%1~=0 and a or s.char((b(a)+b(p:sub(i+1,i+1)))/2))

Try it online!

C (gcc), (削除) 54 (削除ここまで) 51 bytes

-3 bytes thanks to vazt.

Returns a NULL char for empty strings.

l;f(char*s){l=strlen(s);s+=l/2;s=*s+s[l%2-!!l]>>1;}

Try it online!

• \$\begingroup\$ l%2-!!l instead of -!(!l+l%2) for 51 bytes \$\endgroup\$

  vazt

  – vazt

  2018年08月08日 15:29:45 +00:00

  Commented Aug 8, 2018 at 15:29
• \$\begingroup\$ Suggest s=s[l/2]+s[~-l/2+!l]>>1 instead of s+=l/2;s=*s+s[l%2-!!l]>>1 \$\endgroup\$

  ceilingcat

  – ceilingcat

  2018年12月21日 02:58:17 +00:00

  Commented Dec 21, 2018 at 2:58

05AB1E, (削除) 11 (削除ここまで) 15 bytes

Dg≠iÇÂ)øDg;èO;ç

+4 bytes to fix an input of length 1.

Try it online or verify all test cases.

Explanation:

Dg # Duplicate the input, and get it's length
 ≠i # If this length is not exactly 1:
 Ç # Convert each letter to its ordinal value
 # i.e. 'Hiya' → [72,105,121,97]
 Â # Bifurcate (short for Duplicate and Reverse)
 # [72,105,121,97] → [72,105,121,97] and [97,121,105,72]
 ) # Wrap both lists in a list
 # [72,105,121,97] and [97,121,105,72] → [[72,105,121,97],[97,121,105,72]]
 ø # Zip the lists with each other, creating pairs
 # i.e. [[72,105,121,97],[97,121,105,72]]
 # → [[72,97],[105,121],[121,105],[97,72]]
 Dg # Duplicate it, and get it's length
 # i.e. [[72,97],[105,121],[121,105],[97,72]] → 4
 ; # Halve this length
 # i.e. 4 → 2
 è # Index (0-indexed) it in the pairs
 # i.e. [[72,97],[105,121],[121,105],[97,72]] and 2 → [121,105]
 O # Take the sum of the indexed pair
 # i.e. [121,105] → 226
 ; # Halve it
 # i.e. 226 → 113.0
 ç # Convert it from this ordinal value to a character
 # i.e. 113.0 → 'q'
 # (Implicit else: output the 1-char input itself)

Old 11 bytes version which works for all given test cases, but fails for inputs of length 1:

ÇÂ)øDg;èO;ç

Try it online or verify all test cases.

Japt, 15 bytes

cUÊz)dUÔcUÊz1cz

Try it

05AB1E, 5 bytes

ÅsÅAï

Try it online! Beats all other answers. Takes input as a list of codepoints, and outputs as a codepoint.

ÅsÅAï # full program
 ÅA # mean of...
Ås # middle(s) of...
 # implicit input...
 ï # as an integer
 # implicit output

• 1
  \$\begingroup\$ This fails for Hiya. The correct output should be q (113 as ord) \$\endgroup\$

  caird coinheringaahing

  – caird coinheringaahing ♦

  2021年05月13日 20:10:02 +00:00

  Commented May 13, 2021 at 20:10
• \$\begingroup\$ @cairdcoinheringaahing Hmm, good point. I wonder why... I'm looking into it. \$\endgroup\$

  Makonede

  – Makonede

  2021年05月13日 20:12:53 +00:00

  Commented May 13, 2021 at 20:12
• 1
  \$\begingroup\$ It fails because this isn't the median, it's the middle. Median sorts its input \$\endgroup\$

  caird coinheringaahing

  – caird coinheringaahing ♦

  2021年05月13日 20:13:31 +00:00

  Commented May 13, 2021 at 20:13

Python 3.8 (pre-release), 50 bytes

lambda s:chr(ord(s[(l:=len(s)//2)])+ord(s[~l])>>1)

Try it online!

Based on @lirtosiast's answer. Errors out on empty strings and thus the interpreter writes to stderr... So technically no output? O:)

Side note: The parentheses around l:=len(s)//2 are needed because, we are inside brackets [] and Python's parser thinks that the colon is part of a slice? Shouldn't that be a bug since the walrus operator := is a seperate token?

Tcl, 149 bytes

proc C s {expr {$s==""?"":[format %c [expr [scan [lindex [set L [split $s ""]] [set h [expr [llength $L]/2]]] %c]+[scan [lindex $L end-$h] %c]>>1]]}}

Try it online!

• \$\begingroup\$ Failed outgolf, 156: tio.run/… \$\endgroup\$

  sergiol

  – sergiol

  2025年10月26日 19:37:51 +00:00

  Commented Oct 26 at 19:37

• code-golf
• string