Question

The average of $6$ observations is $12$. A new seventh observation is included and the new average is decreased by $1$. The seventh observation is

• A. $1$
• B. $3$
• C. $5$
• D. $6$

Answer 1

The correct option is C $5$

$\Rightarrow$ Let $6$ observations be $x_1,x_2,x_3,x_4,x_5,x_6$.

$\Rightarrow$ The average of $6$ observations is $12$

$\therefore$ $\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}=12$

$\therefore$ $x_1+x_2+x_3+x_4+x_5+x_6=72$ -------- ( 1 )

$\Rightarrow$ Let $7th$ observation be $x_7$

According to the question,

$\frac{x_1+x_2+x_3+x_4+x_5+x_6+x_7}{7}=11$

$\therefore$ $x_1+x_2+x_3+x_4+x_5+x_6+x_7=77$ ---------- ( 2 )

Now, subtractiong ( 1 ) from ( 2 ) we get,

$x_7=5$

$\therefore$ The seventh observation is $5$.