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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
Solution
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
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