x-1, 2x+1, x+5, 3x+1 are in ascending
order. If the median is 18, find the value of x.
Answers
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}⟹Median=
2
(
2
n
)
th
observation+(
2
n
+1)
th
observation
\sf n = 4n=4
\implies\sf Median = \dfrac{\Big(\dfrac{4}{2}\Big)^{th} \: observation + \Big(\dfrac{4}{2} + 1\Big)^{th} \: observation}{2}⟹Median=
2
(
2
4
)
th
observation+(
2
4
+1)
th
observation
\implies\sf Median = \dfrac{2^{nd} \: observation + 3^{rd}\: observation}{2}⟹Median=
2
2
nd
observation+3
rd
observation
\sf 2^{nd} \: observation = x + 52
nd
observation=x+5
\sf 3^{rd}\: observation = 2x + 13
rd
observation=2x+1
\sf Median = 18Median=18
\implies\sf 18 = \dfrac{2x + 1+ x + 5}{2}⟹18=
2
2x+1+x+5
\implies\sf 18 \times 2 = 2x + x + 1 + 5⟹18×2=2x+x+1+5
\implies\sf 36 = 3x + 6⟹36=3x+6
\implies\sf 3x = 36 - 6⟹3x=36−6
\implies\sf 3x = 30⟹3x=30
\implies\sf x = \dfrac{30}{3}⟹x=
3
30
\implies\sf x = 10⟹x=10
Value of x = 10