Median of Set arranged in increasing order 11,12, 14, 15, $x$ + 1, $x$ + 3, 20, 23, 25, 27 is 17, then find the value of $x$?
Solution
arranging set in increasing order
$= 11, 12, 14, 15, x + 1, x + 3, 20, 23, 25, 27$
median = 17 and n = 10
median(M)$\dfrac{\dfrac{n}{2}th~term + \left( \dfrac{n}{2} + 1 \right)th~term}{2}$
$17 = \dfrac{(5th~term)+ (6th~term)}{2}$
$\Rightarrow 17 \times 2 = x + 1 + x + 3$
$\Rightarrow 2x + 4 = 34$
$\Rightarrow 2x = 34 – 4$
$\Rightarrow 2x = 30$
so, $x = 15$
