Sunday, 25 September 2016

Quibans 39: Injured Cyclists

This Quibans is particularly useful when you are working on (revising?) percentages, particularly undoing a percentage change.

From the Cambridge News:
Cyclists injured on Cambridgeshire's roads falls in last year
Shock new figures show more than one cyclist a day was injured on Cambridgeshire's roads last year - but numbers are falling.
Data from the Department for Transport has revealed 444 cyclists were involved in road accidents last year across the county - of which 74 were seriously injured and three fatally.  This is a drop of 6.3 per cent when compared with the ### in 2014, four of which were fatal.
Cambridge also saw a decrease of 4.3 per cent with 221 cyclist injured in 2015.
Noel Kavanagh, Cambridgeshire county councillor and the council's cycling champion, said “These figures are hugely encouraging in light of the fact that there's a large increase in the number of people cycling.”
Elsewhere across the county, there were 44 people injured in South Cambridgeshire last year, a 17 per cent drop and 15 in East Cambridgeshire, a decrease of 28.6 per cent.  But Huntingdonshire saw injuries go up by 15 per cent with 46 cyclists injured on the roads.
Nationally, the number of cyclist injured on the roads as a whole is falling too with ### in 2015, down by 11.5 per cent compared with the 21,287 in 2014.

The first step is to work out the blanked out numbers.  (Answers given below)

Then we could calculate other things, such as the percentage of injuries in Cambridgeshire that take place in the city of Cambridge, the number that were injured in 2014 in different parts of the county, and what percentage of the cyclist injuries across the country occurred in Cambs.


The first missing number is 474.  If students wrongly add on 6.3% then they won’t get the right answer.  This should lead them to think again.

With the second number, even if they do the right calculation they won’t get the given number of 18,845 because of rounding issues.  This is a nice prompt for them to then work out what the actual percentage is (closer to 11.47%).


Friday, 23 September 2016

Quibans 38: Skittles

This Quibans is taken from several sources, including BBC News and the Washington Post.

It is likely many students will have heard about this tweet by Donald Trump’s son:

If you want some of the political reaction to this then you can follow the links below (under ‘sources’).

The BBC article included this:

Here are some figures:
  • Each year, the risk to an American of being killed by a refugee in a terror attack is 1 in 3.64 billion.
  • The manufacturers of Skittles make 200 million of them each day.
  • An ordinary size packet of Skittles contains 54 sweets and 231 Calories (12% of the RDA).
  • An Olympic swimming pool doesn't have a shallow end (!). It has length 50m, width 25m and depth 3m.

What can we work out?

Q1) How much more likely are you to die from choking on food than in a refugee-instigated terror attack?
Q2)  If we want to follow up on the analogy, when there are three poisoned Skittles, how many Skittles are there altogether?
Q3)  What is the total volume of these Skittles?
Q4)  Wikipedia:  "An Olympic-size swimming pool is used as a colloquial unit of volume, to make approximate comparisons to similarly sized objects or volumes."  How many swimming pools do we need to hold the Skittles?
Q5)  How many days will it take to make this many Skittles?
Q6)  How many packets is this?  How many days of calories?
Much of this (and some more probability work too) is covered in the excellent Washington Post article by Philip Bump (link below).  It might be good to ask students to read that article after using this Quibans.


Sunday, 4 September 2016

Quibans 37: Say 'Please'

Here are excerpts from two articles in the Daily Telegraph, published about three years apart.
Polite customers offered cheaper coffee by Spanish café owner
Disenchanted by rude customers, a café owner on Spain’s Costa Brava has introduced a novel incentive to encourage good manners by charging clients according to how polite they are.
A terse demand for “un café” will see guests charged five Euros (£4.20) for a cup of coffee by Marisel Valencia Madrid, the owner of the Restaurant Blau Grifeu in Llança.
Adding please - or por favor - brings the price down to €3.50 (£2.94). Somebody who tries that bit harder and greets the server with a friendly “Buenos días” will only be charged €1.30 (£1.09).
I put a sign in the window with the price system and it has made all the difference. People are now super polite in all matters and it has really improved daily life,” she said.
“Yesterday some children even told their parents to say please, so it’s working!” she added.

French cafe charges rude customers more

11 DECEMBER 2013

A wine bar and bistro in Nice has apparently grown so fed up of rude customers that it's started penalising impoliteness. Ask for "a coffee" in La Petite Syrah, and it costs you €7 (£5.90). Ask for "a coffee please," and the price drops to €4.25 (£3.60). But enter the place crying "Bonjour, a coffee please," - perhaps also embracing everyone within reach- and the cup will cost you what it costs generally in Nice: €1.40 (£1.20).

What can we do with this? [NB: answers/workings are included with the questions below.]

1) We could, clearly, work out the exchange rate. Is it the same exchange rate in both articles?

The first article gives us £1 is approximately €1.19. The second article has three different values (to 2dp) being used.

7 ÷ 5.90 = 1.186441

4.25 ÷ 3.60 = 1.180556

1.40 ÷ 1.20 = 1.166667

The last of these is rather different – and £1.18 would be a more accurate price for that version. The French article seems to have rounded all of the conversions off to the nearest 10p, whereas the Spanish article gave them to the nearest penny.

It is perhaps interesting that the exchange rate from three years ago is very similar to what it is now.

2) Are there any surprises/errors in the articles?

The photograph says that “Adding please - or por favor - brings the price down to €3.50 (£2.94)”, whereas the photograph of the menu shows that this should be €3.

3) How much should this be in sterling (pounds)?

We can use the exchange rate we worked out earlier to get £2.52

4) A ‘very polite’ coffee in Spain has a very similar price to one in France, whereas a ‘rude’ coffee is much more expensive in France. How can we quantify this?

The rude coffee is 40% more expensive in France, the polite coffee is 21% more expensive and the very polite coffee is 8% more expensive.

Alternatively, the rude coffee is 29% cheaper in Spain, the polite coffee is 18% cheaper and the very polite coffee is 7% cheaper.

5) How do these prices compare to the big coffee chains?

The 'London Toolkit' blog has the prices of coffees in the major chains:

You certainly can't get a coffee for £1.20 !

This Quibans could be extended further by carrying out some research into the different varieties of coffee listed here. Are the sizes the same in all three shops? Are the prices the same across England?


Quibans 85: Crime and Police figures

From the Cambridge News: Violent crime in Cambridge has nearly doubled in a decade as police numbers drop 9 APR 2018 Bottom of For...