Find the largest and the smallest number in an array

JavaScript (ES6), 54 56

Edit 2 bytes saved thx @Neil

Note: x===+x is true if and only if x is a number

a=>[Math.max(...a=a.filter(x=>x===+x)),Math.min(...a)]

Pyth, 14 11 10 bytes

hM_BS^I#1Q

Try it online. Test suite.

Explanation

• Q: evaluated input
• #: filter that on:
  • I: the value being the same after:
    • ^…1 raising it to power 1
• S: sort that
• _B: create array [previous, reversed(previous)]
• hM: take first item of each item of that

The hardest part is to golf the removal of strings, which currently takes 4 bytes. The current approach works due to ^<str>1 taking the first Cartesian power of the sequence (basically, the list of the string's characters), but ^<int>1 is just the identity function.

Seriously, 9 6 bytes

,ì;M@m

Try It Online

How it works

,                              Read list input
 ì                             Remove everything but numbers from it
  ;                            Make a copy
   m                           Extract its min value
    @M                         Extract the other one's max value
                               Implicit output (max then min)