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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.
Solution
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
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