Question

The mean of $1,7,5,3,4$ and $4$ is $m$. The observations $3,2,4,2,3,3$ and $p$ have the mean $(m-1)$. Find the median of the second set of data.

• A. $4$
• B. $2.5$
• C. $3$
• D. $5$

Answer 1

The correct option is C $3$

Mean $=m=\frac{1+7+5+3+4+4}{6}=\frac{24}{6}=4$
Now mean of $3,2,4,2,3,3$ and $p$ is $(m-1)=(4-1)=3$
$\therefore \frac{3+2+4+2+3+3+p}{7}=3$
$\Rightarrow \frac{17+p}{7}=3\Rightarrow 17+p=21\Rightarrow p=4$
$\therefore$ The observations are $3,2,4,2,3,3$ and $4$.
Arranged in ascending order, the numbers are $2,2,3,3,3,4,4$.
Median $={\left(\frac{7+1}{2}\right)}^{th}\text{value}=4^{th}\text{value}=3$