When the average is below average

This article the other day (Daily Telegraph, Sydney, 3rd March 2006) caught my eye. Essentially, it is the NSW Government complaining that their grants from the Commonwealth are likely to be cut, because the Grants Commission reckons that they have (amongst other things) an above-average supply of buses.

This caught my eye for a number of reasons. The implication from the article was that NSW was being penalised for having too many buses - or at least more buses than they needed. This raised my hackles at first, since as a long term advocate for public transport I am convinced that what is needed is more buses (and bus services), not fewer.

However, setting that aside, the linguist in me finds it very interesting what is happening here with words. It is clear that what is happening at some level is a conflation of two different meanings of the word average - to the benefit of the Grants Commission beancounters!

In a statistical sense, averages are calculated values. The layperson's "average" is what the statistician would call a sample mean: the sum of observations divided by the count, although occasionally a median (middle value) may be calculated. In either case, it is a numerical construct that indicates a central tendency of a distribution.

I haven't seen the actual Grants Commission data, so I am hypothesising here, but they may have calculated the average number of buses per capita for Australian cities by going to each city that has a bus service, counting the number of buses and dividing by the population (to get per-capita figure for each city) then adding these figures together and dividing by the number of cities to obtain the Australian mean. This is a perfectly reasonable technique, from a statistical point of view.

With this sort of calculation, it is easy to see that Sydney, which has an extensive bus network (particularly in the inner-city) would have a higher number of buses per capita than Melbourne (where the inner city is serviced by tram) or a regional city like Port Lincoln where 1 bus serves 14,000 odd people. Clearly, also, one could expect that the figure for Sydney would be above the average and that for Port Lincoln below the average.

None of this is particularly problematic.

However, words have meaning, and the term "average" has another meaning apart from the statistical. Checking the thesaurus, we find the following entry:

Synonyms: boilerplate, common, commonplace, customary, everyday, fair, familiar, garden, garden-variety, general, humdrum, intermediate, mainstream, mediocre, medium, middling, moderate, nowhere, ordinary, passable, plastic, regular, run-of-the-mill, so-so, standard, tolerable, typical, undistinguished, unexceptional, usual, vanilla, white bread

Using this definition, having an "average" bus service would imply not that the number of buses on the road equalled the arithmetic mean of services around the country, but rather that the service was "moderate", "unexceptional" or "passable". That is to say, the service was nothing to write home about, but at the same time nothing too much to complain about: it is "okay".

Thus we move to the the following statement:

"The Federal Government has been advised to consider NSW as above average in public transport service when it allocates the state's $13 billion GST." (Daily Telegraph, as above - my emphasis) [1].

The economists in the Grants Commission have been able to use the double meaning of "average" to imply that as the number of buses in Sydney is greater than average (above the Australian mean) then the number of buses must be "good" (because "good" is better than "average").

Clearly they are not the same thing at all!

Now it just so happens that my research does show that there is basic, "good enough" level of service for public transport in Australia, where "good enough" means that there are sufficient services to make an impact on car use. It is nothing to write home about (quarter hourly during the day, half hourly at nights and on weekends) and I expect many people would consider it adequate - "average", if you like.

So from a policy point of view, which would you prefer to see? A reduction in services in the big cities to some statistical national "average" level, or an improvment so that everyone gets at least an "average" level of service quality?

I know which I prefer.

[1]This statement also manages to switch from "number of buses" to "level of service". I think this is an acceptable correlation to make, as it is reasonable to assume that the bus companies will have a sufficent number of buses to operate their peak service levels, and not many more. Thus the number of buses is a good first-estimation of services provided.