Question

The mean of 5 observations is 12. If the mean of the first 3 observations is 10, then find the mean of the other two.

Answer 1

Let the observations be a, b, c, d, e.

We know that,
Mean = $\frac{Sumofallobservations}{Numberofobservations}$

Now, mean of 5 observations = 12
$\Rightarrow \frac{a+b+c+d+e}{5}=12$
$\Rightarrow a+b+c+d+e=60$.....(i)

It is also given that the mean of the first three observations is 10.
$\Rightarrow \frac{a+b+c}{3}=10$
$\Rightarrow a+b+c=30$...........(ii)

From (i) and (ii) we get,
d + e = 30

Hence, the mean of the other two observations i.e. 'd' and 'e' is
$=\frac{d+e}{2}=15$