Discussion

Let x be the median of the data

13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.

If 8 is replaced by 18, then the median of the data is y. What is the sum of the values of x and y ?

Answer: C

The sum of x and y is 29.

There are 15 values, so the median is the 8th value in order.

Original data in order: 8, 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17. The 8th value is 14, so x = 14.

Replacing 8 by 18: 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18. The 8th value is now 15, so y = 15.

x + y = 14 + 15 = 29. 28 would follow if the median did not change, which forgets that removing the smallest value shifts every position by one.

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