The geometric mean $($

Qn

i$=1$ ai$)$

$1/$n may cause numerical instability if the products become too large. One

simple way of overcoming this issue is to use the identity

Yn

i$=1$

ai

$!1/$n

$=$ exp

$1$

n

Xn

i$=1$

log ai

$!$

The code chunk below implements the identity above as the function gmean:

gmean $<-$ function$($x$)$ exp$($mean$($log$($x$)))$

Mike would like to compute the geometric mean for each of $10$ columns of a numeric matrix y$.$ He did it

using a for loop, see the code he used in the chunk below.

y$\_$gmean $<-$ numeric$(10)$

for$($i in $1$:$10)\{$

y$\_$gmean$[$i$]<-$ gmean$($y$[,$i$])$

$\}$

Sally saw Mike$$s code and said he could have achieved the same result using vectorisation $($i$.$e$.$ without using

for or while$),$ which is more efficient computationally. Write down a piece of code that would achieve the

same result as Mike$$s code above, but using vectorisation instead of a for loop