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Your comments: Winter 2006

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We would also like to know about your encounters with numbers, whether mystifying, strange or even beautiful.

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Comments from this series

The views expressed on these pages are not necessarily the views of the BBC. The comments published will reflect the balance of views we receive.


School league tables

The measure which is being proposed for CVA is deeply flawed. For example, analysis reveals that students in larger cohorts are more successful than those in smaller ones. This has been built into the model as an environmental factor, so that larger institutions will have to perform better than smaller ones in order to achieve the same value-added result. To put it another way, a student with a particular set of GCSE grades who achieves a particular set of A level results will be judged to have gained a higher value-added score simply by attending a school sixth form instead of a sixth form college or FE college. How can this possibly assist in making a fair comparison between institutions?

This is not the only flaw in the methodology, but it is the easiest to illustrate. The whole thing needs to be taken back to the drawing board, but the government seems determined to press on and simply won't listen to the arguments.
Alan Pucill, UK

At last the issue of education league tables and the 'judgements' that people are invited to make from those has been challenged by this programme. It is a shame that other, more high-profile programmes and presenters have not addressed this issue earlier as it is (IMHO) THE most important one in education. Why? Because education has now become largely a matter of passing through hoops rather than children being properly educated, and the UK will pay an enormously heavy price for this in the next few decades. As a former headteacher, I opposed their ever-expanding role in schools. When they collapse, as they surely will once their detrimental effect has finally been accepted, then don't expect the government of the day to turn to professionals such as me for advice. Oh no ... they'll still be relying on those who got them in this mess ... and carried on digging once they saw themselves in a hole!
John, France

Odometers

One point is to remember tyre wear: eg take a 65 cm diameter tyre. This has a circumference of 204.20cm. Assuming a tread depth of 8mm when new and 3mm when worn, the diameter of a worn tyre is only 201.06 cm, about 1.5% less. That means that the odometer will read about 1.5% more with worn tyres (more revolutions for the same distance) than with new ones.
David Hewitt

As a car tester for the AA over the last 35 years, I must have corrected the indicated speeds and distance recorders of over 1,500 new cars. The inaccuracy of odometers varies from -1.5% to +2.5% on most tested, with less than 10% proving to be spot-on - and another 10% of cars with odometer error greater than the above, mostly on the plus side.

Speedometers are invariably optimistic, nowadays by anything up to 10% - which is particularly galling, when you think about it; it means that the law-abiding motorist who sticks faithfully to the speed limit is actually driving slower than the law requires. In the majority of new cars, this error is built-in to comply with EU rules that permit no speedometer to under-read the true speed, but allows the instrument to over-read by a generous margin.

In fairness to the car-makers, the fact that the same model usually is available with a range of wheels and tyres of varying dimensions, means that the car's overall gearing and therefore its speedometer accuracy will be affected by up to 2%; this still does not justify any greater optimism, however and today's electronically driven instruments could be tweaked for greater accuracy on the production line, in a way that would have been impractical in the past, when both instruments were cable-driven from the gearbox.

It is salutary to remember that a car with a set of over-reading (ie optimistic) instruments will seem to be giving more miles to the gallon - and it will also be taken in for servicing sooner than is strictly necessary! However, there is something we can do to correct both distance and speed indicated by our cars. The UK Motorways have reliable distance posts on the hard-shoulder at intervals of one-tenth of a kilometre - and they are conveniently numbered as well. Listeners to the programme will be quick to realise that when traffic is quiet, the responsible driver armed with a stop-watch and a willing passenger will cover a true 10 miles between 161 posts. In addition, if one times the car at a steady, unvarying speed over 1km/10 posts, then divides the time (in seconds) into 2237, the answer will be one's true speed over the measured distance.
Peter de Nayer

The reason why the new car showed a different distance for travelling to work is simply because the new tyres with the deeper tread have a slightly increased diameter, and hence a slightly increased circumference and so they rotate fewer times for the same distance - I don't expect that the enquirer traded in his old car with brand new tyres!

I have checked this with calculations based on the difference in tread depth and practically by finding that every time I drove down to London to my parents with new front tyres the distance of 210 miles would always be reduced to 208.
Dr Trevor R. Griffiths

Being in the GPS business I happen to have an extremely accurate professional GPS receiver which measures speed to an accuracy of 0.1 mph. I've used it in many different cars and have never found one with a speedometer more accurate than 2% between 30 and 70 mph. Mainly, they're in the 3-6% range, and they always over-read. The odometer, being driven from the same source, has the same accuracy. I'm told by friends in the car trade that this is quite deliberate. It helps to convince drivers they're getting better fuel consumption than they really are and the police like it because drivers think they're going faster than they actually are. The downside is that those pernickety drivers who like to drive at exactly the speed limit are only doing 65, 47, 28 mph etc.

This assumes the car has the correct tyres fitted, they're new and they're properly inflated. A well-worn set of tyres rolls faster (smaller diameter) and makes the difference much bigger - over 10%.
Walter Blanchard

I predict that if your correspondent were to carpool with colleagues on his drive to work, he would seem to travel a longer distance than when he travelled alone! The reason is that the odometer counts the number of wheel revolutions. With a greater weight the tyres are compressed and their effective radius is smaller - more rotations per actual mile, and a greater reading on the odometer! The same would be true in a different car - depending on the tyres installed, their degree of inflation and their wear.
Chris

Cherry Capital Airport

Some thoughts on the Cherry Capital Airport problem:

1. It's a hotbed for hitch-hikers. That is people hitch-hike in, but fly out. As you don't buy a ticket to hitch-hike there is no easy way to count people arriving.

2. There's a perceived benefit to being born there. Hence pregnant women arrive as one but leave as two.

3. People are leaving the area but the effect is masked by a high birth rate.

4. They can't count! Or rather there is some defect in the way in which the data is gathered. Are people arriving as operational air-crew but leaving off-duty and are then counted as passengers? Well alright if this were true there should be lots of 'planes being left there as there's nobody to fly them out. Maybe they need less crew when they leave than they do when they arrive.

5. Are people arriving by bus or boat and then flying out?

6. Is there a problem buying new cars locally? Do you have to fly out and then drive back in your newly bought car?
Philip I'Anson, United Kingdom

The reason why the people leaving any American town by air are less than those arriving could be so many that it is hard to run out of ideas. There could be cases when there are more arrivals that departures, but in many instances:-

  • Some will leave to buy a vehicle that for one reason or another they can buy much cheaper elsewhere, or is not stocked locally. They will return in it.
  • Some will leave by air to arrive urgently where required at short notice, not knowing when the may return, and come back by train.
  • Others will leave to get medical treatment and die away.
  • Some will leave to live elsewhere.
  • Some will be criminals born locally leaving the state to escape the law.
  • Some will be emigrating. People moving in from elsewhere will come with a car if they have one, not by air

The list is endless.

Examine birth and death and population figures, not just airport movements. There is no reason why these should match.
James Baring, UK

Annually around 3,000-4,000 more passengers fly out than fly in. The annual passenger total is 200,000. We have been told that the local population is not shrinking. However, we do not know the local birth or death figures. This would be a good place to look. If the population remains constant then either there must be more births than deaths or the extra passengers must be travelling in. Wikipedia provides a possible clue. The local economy majors on cherries, grapes and tourism. Typical workers in these industries are young and short of money. The industries are seasonal and workers often stay for short periods of time. My suggestion is that the additional air travellers have drifted in by train, greyhound bus or by hitching a lift and after earning some money they can afford to fly out.
David Parkinson, UK

NHS waiting targets

Interesting programme about the corrosive effects of targets. But it doesn't just affect the NHS - it's corrupting the whole of the public sector. I have personal experience of the effect in HMRC [HM Revenue and Customs] and a former colleague now in the police confirms that it applies there as well.

There's a temptation to take the easy option, making it look as though performance is good / improving whilst actual performance is declining.

Senior managers tend to move on before the real effects are recognised.

It's outcomes that count, not outputs, but outcomes are harder to measure objectively and subjective measures of course are out of the question.

You should extend your examination of the subject to the rest of the public sector. Crude performance targets are so corrupting, but the government can hardly complain - they are the experts in spin.
Phil Jones, Wales


Unintended consequences

This week you asked for examples of unintended consequences, I can offer you two, both resulting from the same policy.

Many years ago I worked for a major multinational company and they had introduced a performance rating system where all employees were graded by their managers on a scale of 1 to 5 - 1 being excellent, 5 being a very sad case indeed.

The company also issued an edict that the performance ratings were to conform to the standard bell curve/normal distribution.

However, it was quite genuinely the case that performance ratings were skewed towards the top end (this almost always happens). So, there was a shortage of poor performers; and managers competed with one another to obtain a poor performer or two in order to make their numbers fit.

In short, there was an internal market for poor performers.

The other unintended consequence became apparent when someone in Head Office noticed that in one country nobody was graded more than a 3.

The country manager's explanation for this was that as he himself was graded a 3, he couldn't possibly have anybody working for him whose performance grade exceeded his own.

He managed to present this case as if it were a perfectly logical outcome.
Dr Valerie Stewart, UK

I always remember a story my Dad showed me (unfortunately I don't remember the origins).

Bus drivers were told that they had to do their utmost to stick to their timetables.

Management were soon inundated with complaints about buses whizzing past stops full of people.

When confronted a representative of the drivers said, "Well we can't stick to the timetable if we have to stop and pick up passengers!"

Thanks for an interesting programme.
Stuart Watkinson, Kent


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