The mean of 6 numbers is 32. If one of the numbers is excluded, the mean reduces by 2, then the excluded number is

Given the mean of 6 numbers is 32

Sum of observations $=32\times 6=192$

Given that one of the numbers is excluded

Let the number excluded be $x$ .

Hence the mean reduces by 2

Hence the sum observation  is $192-x$

New observation is 30

$\frac{192-x}{5}=30\Rightarrow x=192-150=42$