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R Statistical Application Development by Example Beginner's Guide by Prabhanjan Narayanachar Tattar

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Letter values

The median, quartiles, and the extremes (maximum and minimum) indicate how the data is spread over the range of the data. These values can be used to examine two or more samples. There is another way of understanding the data offered by letter values. This small journey begins with the use of a concept called depth, which measures the minimum position of the datum in the ordered sample from either of the extremes. Thus, the extremes have a depth of 1, the second largest and smallest datum have a depth of 2, and so on.

Now, consider a sample data of size n, assumed to be an odd number for convenience sake. Then, the depth of the median is (n + 1)/2. The depth of a datum is denoted by d, and for the median it is indicated by d(M)

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