Question

The number $6,8,10,12,13$ and $x$ are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of $x$

Answer 1

Numbers in ascending order are $6,8,10,12,13,x$.
Mean $=\frac{6+8+10+12+13+x}{6}=\frac{49+x}{6}$
No. of terms $\left(n\right)=6$ (even)
Median $=\frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{(\frac{n}{2}+1)}^{th}\text{term}}{2}$
Median $=\frac{{\left(\frac{6}{2}\right)}^{th}\text{term}+{(\frac{6}{2}+1)}^{th}\text{term}}{2}=\frac{3^{rd}+4^{th}}{2}$
$=\frac{10+12}{2}=\frac{22}{2}=11$
According to given condition
$\frac{49+x}{6}=11$
$\Rightarrow 49+x=66$

$\Rightarrow x=17$