Question

If the observations of 6, 7, x-2 ,x,17,20 are written in ascending order and their median is 16. Find the value of'x' .Using the value of x, also find mean of given numbers.

Answer 1

Given if the observations of $6,7,x-2,x,17,20$ are written in ascending order and their median is $16$

$6,7,x-2,x,17,20$

Here observe that no of observations six i.e even

So median is average of ${\frac{n}{2}}^{th}$ term & ${(\frac{n}{2}+1)}^{th}$ term

Median $=\frac{{\frac{n}{2}}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$

$=\frac{{\frac{6}{2}}^{th}term+{(\frac{6}{2}+1)}^{th}term}{2}$

$16=\frac{3^{th}term+4^{th}term}{2}$

$16=\frac{x-2+x}{2}$

$=\frac{2x-2}{2}=\frac{2(x-1)}{2}$

$16=x-1$

$x=16+1$

Value of $x=17$

$\therefore 6,7,17-2,17,17,20$

$6,7,15,17,17,20$

$mean=\frac{sumofobservations}{Noofobservations}$

$=\frac{6+7+15+17+17+20}{6}$

mean $=\frac{82}{6}=13.67$