Question

The following observations has been aranged 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​

Answer 1

Given Observations are

• 13,19,20,25,x,x+2,33,34,35,36

Here,

• Number of observations = 10

• Median of 10 observations = 27

We know,

Median is given by,

$\rm :\longmapsto\:\: Median = \dfrac{1}{2}\bigg( \bigg| {\dfrac{n}{2} } \bigg|^{th} \: obs. + \bigg |{\dfrac{n}{2} + 1} \bigg |^{th}\bigg)$

On substituting the values, n = 10 and Median = 27

$\rm :\longmapsto\:\: 27 = \dfrac{1}{2}\bigg( \bigg| {\dfrac{10}{2} } \bigg|^{th} \: obs. + \bigg |{\dfrac{10}{2} + 1} \bigg |^{th}\bigg)$

$\rm :\longmapsto\:54 = {5}^{th}observation \: + {6}^{th}observation$

$\rm :\longmapsto\:54 = x + x + 2$

$\rm :\longmapsto\:54 = 2x + 2$

$\rm :\longmapsto\:54 - 2 = 2x$

$\rm :\longmapsto\:52 = 2x$

$\bf\implies \:x = 26$

Additional Information :-

Mean of n observations is

$\bf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations }$

Mode :-

• The observation which repeats maximum number of times.

Range :-

• Range = Largest observation - Smallest observation

Answer 2

$\huge\bf\underline\pink{Question}$

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

$\huge\bf\underline\pink{Answer}$

$\large\sf\blue{Given:-}\sf Median\:of\:data=27$

$\large\sf\blue{Data:-}$$\sf 13,\:19,\:20,\:25,\:x\:,x+2\:,33\:,34\:,35\:,36$

$\sf{Number\:of\: observation=10(Even\: number)}$

$\large\sf\blue{To\:Find:-}$Value of x

$\large\sf\blue{Solution}$

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

Where n is the total number of observation

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

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