Rudiments of Numeracy by A.S.C.Ehrenberg - School of Mathematics

1977] EHRENBERG - Rudiments of Numeracy 281has been established. Even now that we know the pattern, it is still not apparent in Table 4.In contrast, anyone can see it in Table 5 (especially anyone already familiar with the notionof a correlation matrix). In fact Table 5 is largely redundant, as with all tables which satisfythe strong criterion of a good table. Its main pattern could be described in words alone, asconsisting of two clusters: correlations of *3 to *6 between the five Sports programmes and of*2 to *5 between the five Current Affairs, with correlations of 1 or so between these twoclusters. Yet some deliberate redundancy in communication usually helps.Experience indicates that most people would agree that the improved tables illustratedhere are somehow better than the original versions. But more formal assessment of this alsoseems desirable-not merely to "prove" the difference, but to see in what ways the improvementswork, for what kinds of people, and under what circumstances. Some exploratorystudies in this direction are summarized elsewhere (Chakrapani and Ehrenberg, 1976).2. Six BASIC RULESThe table improvements illustrated so far involved a combination of factors (subsumed bythe golden rule that the next steps in looking at a table should be visually easy). These factorscan be considered separately and in this section I outline six specific rules or guidelines whichdeal in turn with drastic rounding, marginal averages, choosing between rows and columnsin a table, ordering the rows or columns, the use of space, and the differing roles of graphs andtables.These rules will be illustrated with another example from Facts in Focus (CSO, 1974,Table 97) concerning the level of unemployment in Great Britain over four selected years,as reproduced in Table 6. Although this is again a small and simple table (chosen forconciseness of exposition here), the numerical details are once more not obvious at a glance.TABLE 6Unemployment in Great Britain-Original Version1966 1968 1970 1973Total unemployed (thousands) 330.9 549.4 582.2 597. 9Males 259.6 460.7 495.3 499.4Females 71.3 88. 8 86. 9 98.5Suppose we now look away from this table. What do we remember having seen, withoutlooking back? What can we say about the numbers of unemployed?Rule 1: Rounding to Two Significant or Effective DigitsUnderstanding any set of numbers involves relating the different numbers to each other.But in Table 6 this is not easy. For example, mentally subtracting the 1966 total from the1973 total and remembering the answer is relatively difficult (330 9 from 597'9 = 267.0).Taking ratios mentally (330.9 into 597.9) is virtually impossible. Most of us can do suchmental arithmetic only by first rounding the figures to one or two digits in our heads.In Table 7 this rounding has been done for the reader. The general rule is to round to twosignificant or effective digits, where "significant" or "effective" here means digits which varyin that kind of data. (Final O's do not matter as the eye can readily filter them out.)Now we can see that the difference between 330 and 600 for total unemployed is 270,and that 330 into 600 is almost 2, i.e. an increase of almost 100%. We can also see that theincrease for males from 260 to 500 is again nearly 100%, and that the corresponding increasefor females is about 40%, from 71 to 99. Total unemployed up by almost 100%, males up by