10 observations 6, 14, 15, 7, x+1, 2x-13, 30, 32, 34, 43 are written in ascending order The median - Maths - Statistics

Question

10 observations 6, 14, 15, 7, x+1, 2x-13, 30, 32, 34, 43 are
written in ascending order The median of the data is 24 Find the
value of x

Chetna Khanna · Accepted Answer

Here, the number of observations, n = 10.

Since, n is even, therefore

$Median = \frac{(\frac{n}{2})^{th} observation + (\frac{n}{2} + 1)^{th} obsevation}{2} \Rightarrow 24 = \frac{5^{th} {observation + 6}^{th} observation}{2} \Rightarrow 24 = \frac{(x + 1) + (2 x - 13)}{2} \Rightarrow 24 = \frac{3 x - 12}{2} \Rightarrow 48 = 3 x - 12 \Rightarrow 3 x = 48 + 12 \Rightarrow 3 x = 60$

$\Rightarrow x = \frac{60}{3} \Rightarrow x = 20$

10 observations 6, 14, 15, 7, x+1, 2x-13, 30, 32, 34, 43 are written in ascending order. The median of the data is 24. Find the value of x.