Question

x-1 2x+1 x+5 and 3x+1 are in ascending order if its median is 18 find the value of x​

Answer 1

Question :-

x-1 , x+5 , 2x+1 and 3x+1 are in ascending order. If its median is 18, find the value of x.

Answer :-

Number of observations = 4

If number of observation is even :-

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

• $\sf n = 4$

$\implies\sf Median = \dfrac{\Big(\dfrac{4}{2}\Big)^{th} \: observation + \Big(\dfrac{4}{2} + 1\Big)^{th} \: observation}{2}$

$\implies\sf Median = \dfrac{2^{nd} \: observation + 3^{rd}\: observation}{2}$

• $\sf 2^{nd} \: observation = x + 5$
• $\sf 3^{rd}\: observation = 2x + 1$
• $\sf Median = 18$

$\implies\sf 18 = \dfrac{2x + 1+ x + 5}{2}$

$\implies\sf 18 \times 2 = 2x + x + 1 + 5$

$\implies\sf 36 = 3x + 6$

$\implies\sf 3x = 36 - 6$

$\implies\sf 3x = 30$

$\implies\sf x = \dfrac{30}{3}$

$\implies\sf x = 10$

Value of x = 10

Answer 2

Answer:

Given observations in ascending order

3,6,7,10,x,x+4,19,20,25,28

Here, n=10 which is even and median =13

So,

Median

2

1

[(10/2)thterm+(10/2+1)thterm]=

2

1

(5thterm+6thterm)=

2

1

(x+x+4)=(2x+4)/2=x+2

⇒x+2=13

x=13−2=11

Hence the value of x is 11