Question

The mean of $6$ observations is $54$, including one new observation, the mean is $100$. Find the newly excluded observation.

• A. $176$
• B. $75$
• C. $100$
• D. $56$

Answer 1

The correct option is A $176$

$6$ observations be $s$.
Then mean $=54$.
$54=\frac{s}{6}$
$s=54\times 6=324$
Lets find the newly excluded observation be $X$ then the sum of the observations be $5$,
Mean $=$ $\frac{s+X}{5}$
$100=\frac{324+X}{5}$
$324+X=100\times 5$
$X=500-324$
$X=176$
So, the newly excluded observation be $176$.