Question

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

विकल्प

• 15

• 16

• 17

• 18

Answer 1

The given observations arranged in ascending order are

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

n = 6 (even), median = 16

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

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

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

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

  ${\displaystyle 2x-2=32}$

         ${\displaystyle x=17}$

Hence, the correct option is (c).