Question

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

Given numbers are 34, 37, 53, 55, x, x+2, 77, 83, 89, 100

Here n = 10(even)

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

= `1/2 [ " value of " ( 10/2)^"th" "term" + "value of "  (10/2+ 1)^"th" " term" ]`

= `1/2` [ value of ( 5 )^th term + value of ( 5 + 1)^th term ]

= `1/2` [ value of ( 5 )^th term + value of (6)^th term ]

63 = `1/2` [  x + x + 2 ]

⇒ `[2 + 2x]/(2)` = 63

⇒  x + 1 = 63

⇒ x = 62