Question

The following observation are arranged in ascending order if median of the data is 58. Find the value of x. 28, 31, 48, 51, x, x + 4, 72, 78; 84, 95​

Answer 1

Answer:

x = 56

Step-by-step explanation:

$\huge\blue{\sf{\underline{\underline {Given \: that : - - }}}}$

• 28 , 31 , 48 , 51 , x , x + 4, 72 , 78 , 84 , 95

$\huge\blue{\sf{\underline{\underline {To \: Find : - - - }}}}$

• Find the Value of x ?

$\huge\green{\sf{\underline{\underline {Solution: ---}}}}$

$\large \orange{ \: \tt Given \: observation \: are : }$

$\qquad \qquad \sf \: 28, 31, 48, 51, x, x + 4, 72, 78, 84, 95$

Total number of observations = n = 10 ( which is even number )

Since number of observation is even. Therefore

$\red{ \boxed{ \sf \: Median = \dfrac{ \bigg \lgroup\dfrac{ n}{2} {\bigg \rgroup}^{th} observation \: +\bigg \lgroup \dfrac{n}{2} + 1\bigg \rgroup ^{th}observation }{2} }}$

Putting value of n which is (10)

$\longrightarrow { \sf \: Median = \dfrac{ \bigg \lgroup\dfrac{ 10}{2} {\bigg \rgroup}^{th} observation \: +\bigg \lgroup \dfrac{10}{2} + 1\bigg \rgroup ^{th}observation }{2} } \\ \\ \\ \\ \\ \longrightarrow \sf \: Median = \dfrac{ \bigg \lgroup \cancel\dfrac{ 10}{2} {\bigg \rgroup}^{th} observation \: +\bigg \lgroup \cancel\dfrac{10}{2} + 1\bigg \rgroup ^{th}observation }{2} \\ \\ \\ \\ \longrightarrow \sf \: Median = \dfrac{ \bigg \lgroup 5 {\bigg \rgroup}^{th} observation \: +\bigg \lgroup 6\bigg \rgroup ^{th}observation }{2}$

$\blue{ \large\longrightarrow \sf Media = 58 ( Given)}$

$\qquad \qquad\longrightarrow \sf 58 = \dfrac{x + (x + 4)}{2} \\ \\ \\ \\ \qquad \qquad\longrightarrow \sf58 \times 2 = 2x + 4 \\ \\ \\ \\ \qquad \qquad\longrightarrow \sf116 = 2x + 4 \\ \\ \\ \\\qquad \qquad \longrightarrow \sf116 - 4 = 2x \\ \\ \\ \\\qquad \qquad \longrightarrow \sf112 = 2x \\ \\ \\ \\ \qquad \qquad\longrightarrow \sf2x = 112 \\ \\ \\ \\\qquad \qquad\longrightarrow \sf \: x = \cancel\dfrac{112}{2} \\ \\ \\ \\ \qquad \qquad\longrightarrow \red{\underline{\boxed{\frak{x = 56} \: }}}$

Hence the Value if x = 56