Let x be 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 data is y, then the sum of x and y is equal to:

Arranging the data set in ascending order, it is: 8,9,13,13,14,14,14,14,15,15,15,16,16,17,17

So, total number of terms = 15

So, total number of terms are odd

So, median = $$\left(\frac{n+1}{2}\right)^{th}$$ term = $$\left(\frac{15+1}{2}\right)^{th} = 8^{th}$$ term = 14

So, x=14

Now, if 8 is replaced by 18, then the terms when arranged in ascending order will be like: 9,13,13,14,14,14,14,15,15,15,16,16,17,17,18

So, median = $$\left(\frac{n+1}{2}\right)^{th}$$ term = $$\left(\frac{15+1}{2}\right)^{th} = 8^{th}$$ term = 15

So, y=15

So, sum of x and y = 14+15 = 29