Question

the following observations have been arranged in ascending order .If the median of data is 78 find the value of x. 44,47, 63,x+13,87,93,99,110
​

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

$\sf\underline{\pink{\:\:\:\: Given\:\:\:\:}}$

$\begin{gathered}\sf\bullet Median\:of\:data=78\\ \\ \sf\:\:\:\:\bullet\:\:Data\:is\\ \\ \sf\:\: 44,\:47,\:63,\:x+13,\:87\:,93\:,99\:,110\end{gathered}$

Now we have to find the value of x in the given data

$\sf\bullet{\purple{Number\:of\: observation=8(even\: number)}}$

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

Where n is the total number of observation

$\sf\underline{\red{\:\:\:\: Solution\:\:\:\:}}$

$\begin{gathered}\sf:\implies 78=\dfrac{\bigg(\dfrac{8}{2}\bigg){}^{th}term+\bigg(\dfrac{8}{2}+1\bigg){}^{th}\:term}{2}\\ \\ \sf:\implies 78=\dfrac{\bigg(\dfrac{8}{2}\bigg){}^{th}term+\bigg(\dfrac{10}{2}\bigg)th\:term}{2}\\ \\ \sf\implies78= \dfrac{4th\:term+5th\:term}{2}\\ \\ \sf\bullet 4th\:term=x+13\\ \\ \sf\bullet 5th\:term=87\\ \\ \sf:\implies 78=\dfrac{x+13+87}{2}\\ \\ \sf:\implies 78\times 2=x+100\\ \\ \sf:\implies 156=x+100\\ \\ \sf:\implies x=156-100\\ \\ \sf:\implies x=56\end{gathered}$

The value of x is 56

So 4th observation=56+13= 69

$\huge\mathfrak{\purple{x=56}}$

Answer 2

Answer:

\huge\mathbb{\underline{SOLUTION:-}}

SOLUTION:−

\sf\underline{\pink{\:\:\:\: Given\:\:\:\:}}

Given

\begin{gathered}\begin{gathered}\sf\bullet Median\:of\:data=78\\ \\ \sf\:\:\:\:\bullet\:\:Data\:is\\ \\ \sf\:\: 44,\:47,\:63,\:x+13,\:87\:,93\:,99\:,110\end{gathered}\end{gathered}

∙Medianofdata=78

∙Datais

44,47,63,x+13,87,93,99,110

Now we have to find the value of x in the given data

\sf\bullet{\purple{Number\:of\: observation=8(even\: number)}}∙Numberofobservation=8(evennumber)

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

Median=

2

(

2

n

)

th

term+(

2

n

+1)

th

term

Where n is the total number of observation

\sf\underline{\red{\:\:\:\: Solution\:\:\:\:}}

Solution

\begin{gathered}\begin{gathered}\sf:\implies 78=\dfrac{\bigg(\dfrac{8}{2}\bigg){}^{th}term+\bigg(\dfrac{8}{2}+1\bigg){}^{th}\:term}{2}\\ \\ \sf:\implies 78=\dfrac{\bigg(\dfrac{8}{2}\bigg){}^{th}term+\bigg(\dfrac{10}{2}\bigg)th\:term}{2}\\ \\ \sf\implies78= \dfrac{4th\:term+5th\:term}{2}\\ \\ \sf\bullet 4th\:term=x+13\\ \\ \sf\bullet 5th\:term=87\\ \\ \sf:\implies 78=\dfrac{x+13+87}{2}\\ \\ \sf:\implies 78\times 2=x+100\\ \\ \sf:\implies 156=x+100\\ \\ \sf:\implies x=156-100\\ \\ \sf:\implies x=56\end{gathered}\end{gathered}

:⟹78=

2

(

2

8

)

th

term+(

2

8

+1)

th

term

:⟹78=

2

(

2

8

)

th

term+(

2

10

)thterm

⟹78=

2

4thterm+5thterm

∙4thterm=x+13

∙5thterm=87

:⟹78=

2

x+13+87

:⟹78×2=x+100

:⟹156=x+100

:⟹x=156−100

:⟹x=56

The value of x is 56

So 4th observation=56+13= 69

\huge\mathfrak{\purple{x=56}}x=56