‘Bus Gates’ seem to be the new way to restrict access to certain roads. In the past in Cambridge we had rising bollards that would disappear into the road to allow buses and emergency vehicles to pass through. Bus Gates are ordinary roads, with lots of signs and cameras. A new Bus Gate was installed on what had always previously been a clear section of road. The story below is from the Cambridge News.

Thousands of fines issued to people driving through Mill Road bridge bus gateNearly 5,000 fines have been issued to people driving over Mill Road bridge.

From August 28 to October 16, 4,840 fines have been issued to drivers. The number of drivers themselves being issued with fines will be fewer, since one driver can receive several fines.

Since the summer, Cambridgeshire County Council has closed the bridge to all traffic except buses, cyclists, and pedestrians.

Prior to fines being issued, there was a grace period of more than two weeks when 1,630 notices were sent out to warn drivers that they were committing an offence and should they do so again, then they would face a fine.

The fine is £60, but is reduced to £30 if the motorist pays within two weeks.

More than 96 per cent of fines paid were just £30.

This means the council has made an estimated £151,008 from the partial closure of Mill Road bridge.

The council said last year money from fines was used for frontline highways maintenance.

You might like to present this to a class and to ask what is
wrong with it. Alternatively, the
following questions could lead the students:

Q1) Check every
number. Which ones are exact? Which ones have been estimated by the
journalist?

Q2) How did they do
these estimations?

Q3) Which number is
definitely wrong? Explain!

Q4) Produce a better
version of that number.

Q5) Compare the
number of fines issued to the number of notices sent out during the grace
period. What can we conclude?

Some possible answers follow.

A1) “Nearly 5,000 fines” – has been rounded.

“4,840 fines” and “1,630 notices”. Is it suspicious that the number of fines
(4,840) and notices (1,630) are both multiples of 10? Maybe they have been rounded off? (For both to end in a zero by chance the
probability would be 1/100.) It is
possible that they are exact, though.

The numbers
for the fines are accurate.

“More than
96 per cent” is an estimate, as is “an estimated £151,008”.

A2) 4,840 rounded to the nearest thousand is
5,000.

96% of the
fines were £30. Work out 96% of 4,840
and multiply that by £30. Work out 4% of
4,840 and multiply by £60. Add them
together. We get £151,008.

A3) £151,008.
You can’t possibly get a number that ends in an ‘8’ by adding integer
multiples of 60 and 30.

A4) A better answer/method would be to say: there
are about 5,000 fines and almost all were £30, so that makes a total of 5,000 x
£30 = £150,000. The total is therefore an
estimated £150,000 in fines. I think
this is the best estimate to give. If
you wanted to go more deeply into this we need to decide what the language means. Can we assume “more than 96%” means it’s up
to 96.5%? (suspecting that were to be
over 96.5% then it would be written as “nearly 97%?).

If so, then
a lower bound would be to take 96.5% of the fines as £30 and the rest as £60.

That gives
the newspaper figure as an upper bound (but it would need to be a multiple of
£30) and 150,282 as the lower bound (but again – needs to be a multiple of
30). The bounds would therefore be
150,300 and 150,990. If we assume the
4840 has been rounded to the nearest 10 then that broadens those bounds just a
little. (To be clear, I don’t think any
of this is worth doing: £150,000 is a perfectly sensible estimate here!)

A5) The ‘grace period of more than two weeks’
was presumably there to allow those who use the road regularly to realise that
they would be fined and to warn them of that.
I would expect lots of warnings during the grace period (because it was
a new thing) and fewer fines when it was actually rolled out.

We need to
find the rate for both numbers. August
28 to October 16: That’s 4 days in August, 30 days in Sept and 16 days in Oct:
a total of 50 days. 4,840 fines divided
by 50 days gives an average of 96.8 fines per day. (5000 divided by 50 is perhaps more sensible –
giving 100 per day.)

The grace
period was “more than two weeks”. If
that means 15 days then it is was 108.7 per day, if 16 days then 101.9 per day
and if 17 days then 95.9 per day.

All of
these values are very close to the 96.8 per day that were actually fined. The number of people being fined each day is
the same as the number of people who drove through during the grace period. Does that mean the bus gate just isn’t
working? Or that the fines are not a
deterrent? Or that the grace period was in
August, during the holiday times when the traffic was lower anyway, and that
the massive increase in traffic on the roads in Sept means a smaller percentage
are bursting through the bus gate?

Source: https://www.cambridge-news.co.uk/news/cambridge-news/thousands-fines-issued-people-driving-19173924