# If the median of the data: 6, 7, x − 2, x, 17, 20, written in ascending order, is 16. Then x =

Question:

If the median of the data: 6, 7, x − 2, x, 17, 20, written in ascending order, is 16. Then x =

(a) 15
(b) 16
(c) 17
(d) 18

Solution:

The given observations arranged in ascending order are

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

$n=6($ even $)$, median $=16$

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

$=\frac{3 \text { rd term }+4 \text { th term }}{2}$

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

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

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

$2 x-2=32$

$x=17$

Hence, the correct option is (c).