Question

5. The median of observations 10, 11, 13, 17,
x + 5, 20, 22, 24 and 53 (arranged in
ascending order) is 18; find the value of x.​

Answer 1

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

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

$\sf\bullet Median\:of\:data=18\\ \\ \sf\:\:\:\:\bullet\:\:Data\:is\\ \\ \sf\:\: 10,\:11,\:13,\:17,\:x+5,\:20\:,22\:,24\:,53$

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

$\sf\bullet{\purple{Number\:of\: observation=9(odd\: number)}}$

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

• Where n is the total number of observation

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

$\sf:\implies 18=\dfrac{9+1}{2}th \: observation\\ \\ \sf:\implies 18= \cancel{\dfrac{10}{2}}th\:term\\ \\ \sf:\implies 18=5th\:term\\ \\ \sf\:\:\:\bullet 5th\:term= x+5\\ \\ \sf:\implies 18=x+5\\ \\ \sf:\implies 18-5=x\\ \\ \sf:\implies x=13$

The value of x is 13

$\huge\mathfrak{\pink{x=13}}$