The median and interquartile range of a set of data is shown. Write a set of data consisting of seven values for the pair of measures. Median: 5 Interquartile Range: 5

If there are 7 data points (an odd number), then the median, 5, is right in the middle of the 7 points:  x y z 5 q r s.

If the IQR is 5, we then know that the difference between y and r is 5.

Let's find the 1st and 3rd quartiles.  Focusing on the 1st 3 numbers, we see that the 1st quadrant is y; focusing on the last 3 numbers, we see that the 3rd quadrant is r.  The IQR is r-y = 5.  Just supposing that y were 4, r would be 9:

x 4 y 5 q 9 s

We could arbitrarily let x = 3, y = 4, q = 5 and s = 9:  3 4 4 5 5 9 9.

We must check this!  
What is the median?  Since there are 7 numbers here, we take the middle number (5) as the median.  This agrees with the problem statement.
Next, we find Q1 and Q3.  Q1 is the number between 3 and the 2nd 4, and is 4.  Q3 is 4+5, or 9, because the IQR is 5.  This agrees with the problem statement.