Question

The following observations have been arranged in ascending order. If the median of these observations is 58, find the value of x.

24, 27, 43, 48, x - 1, x + 3, 68, 73, 80, 90

Answer 1

Consider the given data:

24, 27, 43, 48, x - 1, x + 3, 68, 73, 80, 90.

Here the number of observations is 10, which is even.

Median = `((n/2)^"th" + (n/2 +1)^"th")/2`

58 = `((10/2)^"th"+(10/2+1)^"th")/2`

58 = `(5^"th"+  6^"th")/2`

58 × 2 = x - 1 + x + 3

116 = 2x + 2

116 - 2 = 2x

114 = 2x

x = `114/2`

x = 57