Question

if median of the following data is 63,find the value of x ???

29 , 32 , 48 , 50 , x , x+2 , 72 , 78 , 84 , 95 .

Answer 1

No : of observations , n = 10 (even)
median of even no:s = [n/2 th observations + n+1 / 2 th observations] ÷ 2

n/2 th observation = 10 ÷ 2 = 5 th observation = x

n+1 / 2 th observation = 6 th observation = x +2


median = [ x+x+2] ÷2
[ x+x+2] ÷2 = 63
[2 x+ 2] ÷ 2 = 63
2 x+ 2 = 63 × 2
2 x+ 2 = 126
2 x = 126 - 2
2x = 124
x = 124 ÷ 2 = 62


∴ x = 62


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Answer 2

Number of observations, n  = 10 (even)

Median = (n/2 th term + n/2 + 1 th term)/2
63 = (10/2 th term + 10/2 + 1 th term)/2
63 = (5th term + 6th term)/2
63 = (x + x + 2)/2
126 = 2x + 2
2x = 124
x = 62

Value of x  = 62

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