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X-1, 2x+1, x+5, 3x+1 are in ascendingorder. If the median is 18, find the value of x. |
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Answer» 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 |
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