Question

The mean of first $8$ observations is $18$ and last $8$ observations is $20$. If the mean of all $15$ observations is $19$, find the $8^{th}$ observation

• A. $18$
• B. $12$
• C. $19$
• D. $20$

Answer 1

Answer: (C)

$19$

$\frac{a_1+a_2+...a_8}{8}=18;\frac{a_8+...a_{1}5}{8}=20$ __(1)

$

$\frac{a_1+...+a_{15}}{15}=19$ __(2)

From (1)

$a_1+a_2+....+a_{15}=(18+20)8$

$\Rightarrow (a_1+a_2+...+a_{15})+a_8=38\times 8$

From (2)

$19\times 15+a_8=38\times 8$

$\Rightarrow a_8=19$