The Little Blue Reasoning Book - Brandon Royal [18]
Matrixes vs. Tables
Confusion often arises regarding the use of tables and matrixes. While it is true that matrixes look like tables (actually, all matrixes are tables but not all tables are matrixes), they are distinctly different tools. As previously illustrated, matrixes must total across and down and do so because the data or information contained in them is mutually exclusive and collectively exhaustive. Tables simply display or group related information. However, tables should not be used to sort random data.
Table A works well because the information is related. Here, the study of marketing is displayed by breaking it down into four distinct areas.
Table A – The Marketing Mix
The information in Table B is not presented effectively because the words appear random and arbitrary.
Table B – Medical Discoveries in Europe
The cities mentioned above should, in all likelihood, be enumerated in a list:
1. Paris
2. London
3. Madrid
4. Amsterdam
Exhibit 3.3 is not a matrix (although it certainly looks like one) because the information only “reads” down, but not across. The following write-up would likely accompany this table or chart:
We hear so much about information today. But when is information deemed “good” information? Information is best understood by looking at it in terms of its four quality dimensions — accessible, summarized, relevant, and customized. When information touches all of these dimensions it becomes both efficient and effective.
The dimensions of “accessible” and “summarized” relate to the efficiency of information. The dimensions of “relevant” and “customized” relate to the effectiveness of information. The terms effective and efficient are, in casual conversation, often used interchangeably because information has traditionally been thought to be effective as soon as it has been deemed efficient — that is, when “accessible” (dimension 1) and “summarized” (dimension 2). It is the purpose of this chart to highlight the importance of effectiveness — “relevant” (dimension 3) and “customized” (dimension 4). Unless information is effective as well as efficient, it will not be easily adopted or internalized by the user. Without becoming effective, information cannot be easily recalled or acted upon. Information that has all four elements may be said to be “transparent.” It is so ready and usable that it takes on the appearance of always being in the mind of the user.
Exhibit 3.3 – The Effective Information Paradigm
Using Matrixes
Job search: Of thirty-five applicants applying for a job, twenty had at least seven years’ work experience, twenty-three had degrees, and three had less than seven years’ work experience and did not have a degree. How many of the applicants had at least seven years’ work experience and a degree?
Step #1: Sketch a matrix and enter given information into the appropriate boxes. The shaded box depicts the value we’re trying to find.
Step #2: Let’s total the numbers on the side and bottom of the matrix, filling in the dotted boxes.
Step #3: Since data must total down and across, we simply fill in remaining numbers within the middle four boxes.
Eleven of the candidates, therefore, have at least seven years’ work experience and hold degrees.
For each of the following problems, use matrix analysis to calculate the desired outcomes.
Problem 7: Singles
In a graduate physics course, 70% of the students are male and 30% of the students are married. If 20% of the male students are married, what percentage of students are female and single?
See solution
Problem 8: Batteries
For every batch of 100 batteries manufactured at a certain upstart factory, one-fifth of the batteries produced by the factory are defective and one-quarter of all batteries produced are rejected by the quality control