Chapter 3: Summarizing Data

In this chapter, we will discuss the process that one follows to maximize information, given a set of data. We will describe several ways of presenting data for communicating analysis results that will make more sense than presenting the data in their raw form.

OVERVIEW

In recent years , quality decisions have come to depend more and more on the analysis of data. This includes the supervisor or the person on the line who may need information about the department or the process that he or she is serving. This trend in the use of data for a better outcome of a process is due partially to our awareness for a better overall quality as well as to the increasing availability of high-speed computers. Indeed, some of the data-processing techniques would have been impossible to generate or track without the use of computers in the floor-level (job-level) environment.

First, by reorganizing the data in a predefined group (or, as in some cases, classes), we often gain much information, as in this example.

Daily Diameter Difference (in thousands)	Number of Grind Bearing Diameters
under 80	21
80 “89	114
90 “99	182
100 “109	290
110 “119	204
120 “129	159
130 “139	88
140 “149	74
150 “159	45
160 or more	39
Total	1216

The data that have been grouped here are a sample of daily diameter differences over a one-week period. This kind of table is called a frequency distribution, and it shows the frequencies with which the diameters are distributed among the chosen classes. Tables of this sort , in which the data are grouped according to numerical size , are called numerical or quantitative distributions.

In contrast, tables like the one given below, in which the data are sorted according to a number of categories, are called categorical or qualitative distributions.

Category of Defects	Number of Defects
Too soft	340
Poor micro finish	891
O.D. too large	941
O.D. too small	379
Total	2551

Although frequency distributions present data in a relatively compact form, give a good overall picture, and contain information that is adequate for many purposes, there evidently are some things that can be obtained from the original data and that cannot be obtained from the distribution. For instance, in our first example, we can find neither the lowest and highest of the diameter differences nor the exact average of the number of grinds of the 1216 pieces. Nevertheless, frequency distributions present raw (unprocessed) data on which they are based in a more usable form, and the price that we must pay, the loss of certain information, is usually a fair price.

Data are sometimes grouped solely to facilitate the calculation of further statistical descriptions. You will learn more about that in the next chapter, but it is worth noting that this function of frequency distributions is diminishing in importance in view of the ever-increasing availability of computers and their application to high-level statistical analysis.