Question

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The following observations has been arranged in ascending order . If the median of the data is 27 , Find the value of x 13,19,20,25,x,x+2,33,34,35,36​



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Answer 1

Given :-

• $\sf Median\:of\:data=27$
• $\sf Data\:is:-13,\:19,\:20,\:25,\:x\:,x+2\:,33\:,34\:,35\:,36$
• $\sf{Number\:of\: observation=10(Even\: number)}$

Need To Find Out :-

• Value of "x

Solution :-

$\red {\boxed{\sf{Median=\dfrac{\bigg(\dfrac{n}{2}\bigg){}^{th}\:term+\bigg (\dfrac{n}{2}+1 \bigg){}^{th}\:term}{2}}}}$

• Where n is the total number of observation

$\sf:\implies 27=\dfrac{\bigg(\dfrac{10}{2}\bigg){}^{th}term+\bigg(\dfrac{10}{2}+1\bigg){}^{th}\:term}{2}\\ \\ \sf:\implies 27=\dfrac{(5){}^{th}term+(6){}^{th}term}{2}\\ \\\sf \leadsto 5th\:term=x\\ \\ \sf \leadsto 6th\:term=x+2\\ \\ \sf:\implies 27=\dfrac{x+x+2}{2} \\ \\ \sf:\implies 27\times 2=2x+2 \\ \\ \sf:\implies 54=2x+2\\ \\ \sf:\implies 2x=52\\ \\ \sf:\implies x=\cancel{\dfrac{52}{2}} \\ \\ \sf:\implies\red {\underline{x=26}}$

$\underline\purple{{\boxed{\mathsf{The \: value \: of \: x \: is = 26}}}}$