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14.
To find the IQR, first find the median of the data set. In this case, the median is the average of the middle two numbers: (77+81)/2 = 79.
Next, divide the data set into two halves: {61, 65, 75} and {81, 83, 85, 87}.
Find the median of the lower half: (65+75)/2 = 70.
Find the median of the upper half: (83+85)/2 = 84.
Subtract the lower median from the upper median: 84 - 70 = 14.
So, the IQR of the data set is 14.