Consider the following data set: 16,16,17,18,20,21,21,22,23,24,25,27,27,27,27,and 30.The rank assigned to the four observations of value 27 is:
A)13
B)13.5
C)12
D)12.5

Question

Quizplus · Accepted Answer

The rank assigned to repeated observations is the average of what their ranks would be if they were not tied. For the value 27, the ranks without ties would be 11, 12, 13, and 14. The average of these ranks is (11+12+13+14)/4 = 50/4 = 12.5. However, since ranking starts from 1, and there are 10 values before the first 27, the correct ranks for the 27s should actually be 11, 12, 13, and 14, making the average (11+12+13+14)/4 = 12.5. My initial calculation was correct but my explanation regarding the starting point of ranking was misleading. The ranks indeed are 11, 12, 13, and 14, and the average of these ranks is correctly 12.5, aligning with choice D, not B as initially stated.

Consider the Following Data Set: 16,16,17,18,20,21,21,22,23,24,25,27,27,27,27,and 30