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Road transport statistics the hazards of averages
Page 108
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THE sheer welter of road transport statistics produced in surveys, traffic counts and Ministry figures, can all too easily cause bewilderment and discouragement. It is obviously necessary to summarize many of the tables of figures presented in such a way that the essence is retained. The big problem is how to distil the information so that it can be used to throw light on the problem with which one is involved. For examination purposes, too, reproduction of lengthy data is both out of place and time-wasting in answering questions—a short and succinct presentation of the essentials is required.
The obvious instinct is to cut down the figures presented and reduce them to averages. But the word "average" covers a multitude of conditions and in formal statistics there are three quite separate and recognizable types of averages—(a) the arithmet ic mean, (b) the mode and (c) the median.
As I noted last week the arithmetic mean is the average nearly always used by those unskilled in the ways of statistics. It is the least satisfactory average and very often distorts rather than simplifies the data. In one of the few surveys made of carrying capacity of goods vehicles carried out by the Ministry of Transport Survey in 1962 (published variously between 1964 and 1966), a quite irrelevant figure would be obtained if an arithmetic mean was used. For example, in the analysis of carrying capacity of C-licensees in 1962 (normally the figures are for unladen weight), an arithmetic mean could be derived by adding up the total carrying capacity of whole fleet and dividing by the number of vehicles thus arriving at the "average" carrying capacity per vehicle. The figure obtained would be
useless as no indication could be given or the high proportion of small vehicles with a tiny carrying capacity—in 1962, 785,400 vehicles in this category were not over 1 ton gross weight in a total fleet size of 1,226,400 vehicles.
In the Ministry of Transport Highway Statistics for 1967 (the most recent figures) no purpose would be served_ either, by calculating the arithmetic mean of unladen weight per goods vehicle since slightly more than half the total number of goods vehicles in that year had an unladen weight of 1+ tons. Worse problems affect statistics on bus size since the Ministry figures include taxis as well as buses under the category "public transport vehicles". Thus, the high proportion of vehicles with a seating capacity of four persons or under would result in the average seating capacity per vehicle obtained through an arithmetic mean being an entirely irrelevant statistic.
Much more apposite is the mode which is the average expressing the most frequently occurring type. In the case of the original example of the C-licence carrying capacity in 1962. the mode would clearly show that the category "under one ton" was the most typical carrying capacity.
In the same example, the median is the middle-sized C-licensed vehicle obtained by arranging all the 1,226,400 vehicles in order of capacity and finding the middle one. Thus, half the vehicles will be larger and half will be smaller. In this example, it will be the 613,200th vehicle which will be in the middle once they have been arranged in size. As the figures in this survey do not give the exact capacity of each vehicle, it is not possible to be precise about the median vehicle, but it must be less than one ton in capacity since more than half are in that category. Thus, the mode and the median give much more significant summarized information than the traditional average obtained through the arithmetic mean.