Average Length of Google
Bash + system utilities, 56 53 49 48 bytes

Update: saved 4 bytes thanks to Digital Trauma and 1 byte more thanks to Dennis

curl -L `yes google.com|sed $1q`|wc|dc -e1k?$1/p


In my original answer I was using yes in combination with xargs to emulate a for loop. But curl can accept as input a list of URLs, so only the output from yes is actually needed.

When curl accesses google.com, it receives a 302 redirection page that has the new URL in the body section, so the -L option is needed to follow it.

Run example: answer is printed to STDOUT, I redirect STDERR just for clarity

me@LCARS:/PPCG$ ./google_length.sh "8" 2&gt; /dev/null
10583.2


Explanation: (of the initially submitted code)

yes google.com|     # repeatedly output a line containing the string "google.com"
sed $1q|            # print the first $1 lines only (shorter than head -$1)
xargs curl -sL|     # xargs reads the input lines and executes "curl -sL" with the
                    #current input line as an additional argument.
wc -m|              # count the number of characters
dc -e1k?$1/p        # dc script: set precision to 1, read input, push $1 and divide


Edit: I replaced wc -m with wc, because even if without arguments it prints 2 more statistics than the one I wanted, the same dc script following this output still works, because the count we want is, happily, placed on top of the stack during parsing.