Question

The following numbers 3, 7, 12, x-1, x+3, x+4, 20, 24 are arranged in ascending order. Find the value of x, if their median is 16. *

A.4.5
B. 13
C. 16
D. 15​

Answer 1

Answer :-

If number of terms are even -

$\sf Median = \dfrac{\Big(\dfrac{n}{2}\Big)^{th} \: observation + \Big(\dfrac{n}{2} + 1\Big)^{th} \: observation }{2}$

Here, n = 8

⇒ $\sf \dfrac{n}{2}$ = 4th observation = x - 1

⇒ $\sf \dfrac{n}{2} + 1$ = 5th observation = x + 3

Now, we are given median of the data, so by using the formula we can find the value of x :-

⇒ $\sf \dfrac{x - 1+x + 3}{2} = 16$

⇒ $\sf \dfrac{2x + 2}{2} = 16$

⇒ $\sf 2x + 2 = 32$

⇒ $\sf 2x = 30$

⇒ $\sf x = \dfrac{30}{2}$

⇒ $\sf x = 15$

Value of x = 15