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Question
If 12, 16, 18, x + 2, x + 4, 45, 48, 52 are arranged in ascending order and their median is 31, find the value of x.
Sum
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Solution
Given: 12, 16, 18, x + 2, x + 4, 45, 48, 52 are in ascending order and median = 31.
Step-wise calculation:
1. There are 8 numbers, so the median is the average of the 4th and 5th terms `n/2`th and `(n/2 + 1)`th.
2. 4th term = x + 2 and 5th term = x + 4.
So median = `[(x + 2) + (x + 4)]/2`
= `(2x + 6)/2`
= x + 3
3. Set x + 3 = 31
x = 28
4. Check order: x + 2 = 30 and x + 4 = 32, which lie between 18 and 45, so the given ascending order is valid.
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Notes
The answer in the textbook is incorrect.
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