Question

For Exercises rank each set of data.

19.4, 21.8, 3.2, 23.1, 5.9, 10.3, 11.1

Answer 1

Nonparametric statistics uses data that is often ordinal, meaning it does not rely on numbers, but rather on a ranking or order of sorts. A very effective and widely used approach is to transform the data values into ranks and work with the ranks of the data instead of the actual observations.

 

By ranking the data, the impact of outliers is mitigated; regardless of how extreme an outlier is, it receives the same rank as if it were just slightly larger than the second-largest observation

 

Step 1: Arrange the given data in ascending order.

Before giving ranks to the dataset, we arrange the data values from smallest to largest as follows:

Data

3.2

5.9

10.3

11.1

19.4

21.8

23.1

 

Step 2: Start giving ranks to the given data. The lowest value here is assigned the rank 1 and the second lowest value is assigned the rank 2 and so on.

Now we assign ranks to data values starting from rank 1 to the smallest data value 3.2, rank 2 to the second smallest data value 5.9, so on till rank 7 to the largest data value 23.1.

Data	3.2	5.9	10.3	11.1	19.4	21.8	23.1
Ranking	1	2	3	4	5	6	7