Question

2. The following data have been arranged in
ascending order. If their median is 63, find the
value of x.
34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.​

Answer 1

$\huge\mathbb{SOLUTION:-}$

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

$\sf\bullet Median\:of\:data=63\\ \\ \sf\:\:Data\:in\: ascending\: order\\ \\ \sf\bullet 34,\:37,\:53\:,55\:,x\:,x+2\:,77\:,83\:,89\:,100$

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

$\sf\bullet n=Number \:of \:observation\\ \\ \sf\bullet n=10$

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

$\sf:\implies 63=\dfrac{\dfrac{10}{2}+({\dfrac{10}{2}+1)}}{2}\\ \\ \sf:\implies 63=\dfrac{\cancel{\dfrac{10}{2}}+({\cancel{\dfrac{12}{2})}}}{2}\\ \\ \sf:\implies 63=\dfrac{5{}^{th}\:term+6{}^{th}\:term}{2}\\ \\ \sf\:\:\: 5{}^{th}term=x\\ \\ \sf\bullet \:6{}^{th} term=x+2\\ \\ \sf:\implies 63=\dfrac{x+x+2}{2}\\ \\ \sf:\implies 63\times 2=2x+2\\ \\ \sf:\implies 126=2x+2\\ \\ \sf:\implies 126-2=2x\\ \\ \sf:\implies 124=2x\\ \\ \sf:\implies \cancel{\dfrac{124}{2}}=x\\ \\ \sf:\implies x=62$

$\huge\boxed{\mathfrak{\purple{x=62}}}$

Answer 2

$\mathfrak \purple{solution}$

Given,

• Numbers are 34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100(data is already given in ascending order)
• median =63

Here n =100(even no.)

$\mathbf \red{formula}$

Median=1/2[value of (n/2)th term + value of (n/2+1)th term]

NOW,

putting the value....

Median=1/2[value of (10/2)th term+value of (10/2+1)th term]

=>63=1/2[value of (5)th term+value of (5+1)th term]

=>63=1/2{value of (5)th term+value of (6)th term]

• 5th term=x
• 6th term=x+2

=>63=1/2[x +x+2]

=>63=1/2[2x+2]

=>63=x+1

=>x=63-1

x=62