Chapter 13: Missing Data

Chapter 13: Missing Data

Overview

In a perfect mathematical model, we know everything. However, the real world is not a perfect mathematical model. There will be values of attributes that are missing from our database.

The Interim Report 75-02-08 to the ANSI X3 (SPARC Study Group 1975) had 14 different kinds of incomplete data that could appear as the result of queries or as attribute values. These types included overflows, underflows, errors, and other problems in trying to represent the real world within the limits of a database.

People have trouble with things that are not there. It took centuries for Hindu-Arabic numerals (with the new concept of zero) to surpass the zeroless Roman numerals in popularity in Europe. In fact, many early Renaissance accounting firms advertised that they did not use the fancy, newfangled notation and kept records in well-understood Roman numerals instead.

Many of the conceptual problems with zero arose from not knowing the difference between ordinal and cardinal numbers. Ordinal numbers measure position; cardinal numbers measure quantity or magnitude. The argument against the zero was this: If there is no quantity or magnitude there, how can you count or measure it? What does it mean to multiply or divide a number by zero?

Likewise, it was a long time before the idea of an empty set found its way into mathematics. The argument was that if there are no elements, how can you have a set of them? Is the empty set a subset of itself?

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