Saturday, 24 December 2016

Quibans 51: Monster Carrots

From the Cambridge News:
Frenzied Friday: Supermarkets to see surge in last minute food shoppers before Christmas
Supermarkets across the country are bracing themselves for rush of last minute Christmas food shoppers today (December 23).
Already dubbed 'Frenzied Friday', many stores are expected to have their busiest day of the year as millions of customers stock up for some Christmas feasting.
Tesco's has predicted that over 10 million customers will be visiting its stores throughout the day, around 15,000 per minute.
Tesco expects to selling 40 million Brussels sprouts across today and yesterday as well as 3.5 million carrots - enough to stretch around the world 11 times.

The big thing here is having an idea about the size of numbers. An initial question (before showing the other questions):

Question zero) Do the numbers in the question seem reasonable ones?


Questions:


Q1) “10 million customers […], around 15,000 per minute”. What does this tell us?

Q2) The distance from the north pole to the equator is 10,000 km. How big would a carrot need to be if the news story is accurate?


Answers:

Q0) The number of customers seems reasonable, but the number of carrots seems to be much too small to stretch around the world 11 times.

Q1) 10 million divided by 15,000 equals just over 11 hours. So either Tesco stores are open for 11 hours a day, or they have sensibly decided that more people shop during the day rather than in the middle of the night.

Q2) The circumference of the earth is 40 million metres. 11 times round the world would be 440 million metres. Dividing that by 3.5 million carrots gives an average carrot-length of 126 metres. Monster carrots! 12.6cm seems more reasonable for the length of a carrot so dividing by 1000 would be useful.

There are three easy ways to do this: make an error and assume the circumference of the world is actually 40,000 metres (rather than km); sell 3.5 billion carrots, or say that the carrots will go 0.011 times round the world!

If you decide that the Brussels sprouts should be included (the sentence is potentially ambiguous, even if you ignore the grammatical typo) then that doesn’t help (unless you have Monster Sprouts…).

Source: http://www.cambridge-news.co.uk/news/cambridge-news/frenzied-friday-supermarkets-see-surge-12364134


Friday, 16 December 2016

Quibans 50: A million cyclists

From the Cambridge News:
One million cyclists in Cambridge have passed Parker's Piece bike counter this year
14 Dec 2016
One million cyclists have ridden past the cycle counter in Parker's Piece since January, breaking the all-time record.
 
Roxanne de-Beaux, of the Cambridge Cycling Campaign, said last year the total had fallen frustratingly short, coming in 50,000 under the million mark.
Cllr Noel Kavanagh, cycling champion at Cambridgeshire County Council, said the number was brilliant news, but not a total surprise.
"I am not surprised," he said. "I cycle through it several times and have noticed the total going up. Most days, it is two or three thousand. I think this is really good.”
The counter was put in place in 2014, in part to commemorate the historic start of the 2014 Tour de France in the city.

Here are some of the comments under the article:

Commenter 1:
Interesting to note that a person who uses their car exclusively probably pays less per mile in VED, than a car owning cyclist... in other words, a car owning cyclist pays more "road tax" per mile than average Joe Car.
Commenter 2:
"a car owning cyclist pays more" - interesting, I never thought of it like that.
Commenter 1:
I have a car and a bicycle. I do ~2000 miles in my car (I cycle most places within 5 miles) and pay ~£220 VED, thus pay ~##p per mile.
The average car does around 8000 per year, with an average VED of £166, so ~##p per mile. (source for averages... Google).
So, thus as mainly a cyclist in town, I pay a lot more road tax per mile than most car drivers. Given, there are a lot of caveats to this.


The comments under a Cambridge News article that involve bikes often turn into a cyclist vs driver argument. This little exchange between two commenters involves some nice Core Maths skills!

Possible questions:


1) What does the headline mean?

2) How many bikes pass this point per day? What are the difficulties with carrying out this sort of calculation?

3) What will the counter read at the end of the year?

4) What is the percentage increase from last year?

5) Is the councillor correct with his statements?

6) VED is “vehicle excise duty” – commonly referred to as “car tax” or “road tax”. The symbol ~ means “approximately”. What are the numbers I have blanked out in the comments?



Answers:


1) It doesn’t mean that there were a million cyclists. Just that a bike has been read by the sensor a million times. One person cycling past it twice each day would contribute 365 x 2 of these, for example.

2) There are 31-13 = 18 days to go until the end of the year. This was a leap year, so there have been 366-18 = 348 days. 1 million divided by 348 = 2874 per day.

I have no idea whether more people cycle during the week (getting to work), or at the weekend (because they have time to do so). Maybe best to say it is between 2500 and 3000 per day?

We also don’t know when the figure of a million was reached (we only have the date of the article to go on.)

3) What will the counter read at the end of the year? Again, we don’t know whether more people cycle close to Christmas (for leisure reasons, coming back from Christmas parties, etc), or fewer (they drive because they won’t fit the presents they buy in their basket, they are away visiting relatives, etc. If we go for 2500 per day between now and the end of the year then that would be an additional 45000.

4) What is the percentage increase from last year? 1,045,000 this year compared to 950,000 last year. Dividing these gives 1.1, which means a 10% increase.

5) Is the councillor correct with his statements? “have noticed the total going up” – yes- that is correct (!). “Two or three thousand” is right too.

6) ~11p compared to ~2p.



Source: http://www.cambridge-news.co.uk/news/cambridge-news/record-breaking-one-million-cyclists-12321840

Saturday, 10 December 2016

Quibans 49: Bike thefts

From the Cambridge News:

Cambridge branded bike theft capital and rail station ranked third worst cycle theft hotspot

Criminals swiped 2,173 cycles in 12 months and streets within the city account for 13 of the top 100 bike theft hotspots listed in police recorded crime data, more than any other local authority area.

The top hotspots for theft are Station Road at the railway hub with 63 thefts, and Parkside, next to the city police station and Parker’s Piece, with 62, following new analysis of crime data from every police force in England and Wales analysed by online insurer Protect Your Bubble.

The bike theft problem in Cambridge is underlined when the thefts are calculated per 1,000 residents. The overall rate for England and Wales is 1.4 thefts per 1,000 people. In Cambridge it’s 16.6.

Government figures show that across England 9.5 per cent of adults cycle at least once a week. But Cambridge is way ahead of other cities with 52 per cent.


Questions
Can students create their own questions?
Here are mine:
1) What percentage of bikes stolen in Cambridge were taken from Parkside (near the police station)?
2) How many residents does Cambridge have?
3) Roughly how many people in Cambridge cycle at least once a week?

Answers
1) 62/2173 = 2.85%
2) (2173/16.6) * 1000 = 130,904 (This is very close to the official figure of 130,907 and rounding is likely to be the issue.)
3) Hmm. The article says that 52% of _adults_ cycle at least once a week. If we assume that the same is true of children then we would get about 65,000. If more children cycle then it will be a little higher.

Source: http://www.cambridge-news.co.uk/news/cambridge-news/cambridge-branded-bike-theft-capital-12264943

Quibans 74: Parking fines

The article below is excerpted from the Cambridge News website (link at the foot of the page). Read the article, carry out some calculati...