Saturday, 18 November 2017

Quibans 73: Food waste

Here are excerpts from four Guardian articles, all from 2017. The original headlines are shown in bold.

Nearly half of all fresh potatoes thrown away daily by UK households

Nearly half of the edible fresh potatoes bought by UK householders each day are thrown away - 5.8 million of them per day, and at a “staggering” annual cost of £230m, figures show.

The humble spud is the second most wasted food in the UK, behind bread, according to campaign material released on Wednesday. The research was offered in support of a government campaign to encourage consumers to reduce their domestic food waste.

The UK churns out 10m tonnes of food waste a year – of which 7.3m tonnes come from households. The estimated retail value of this is £13bn, and Wrap calculates that a typical family wastes £700 of food a year.

Britons to throw away £428m worth of barbecue food in August, study reveals

It’s symbolised by dismal burgers and carbonised sausages served on paper plates with a splatter of ketchup. Yet with the great British summer well under way, Britons are this month set to throw away a staggering £428m worth of barbecue food, research reveals.

In August the nation will brave the changeable weather to enjoy nearly 12m barbecues, with people on average either hosting or attending at least two of the seasonal gatherings. The new research from supermarket chain Sainsbury’s shows that hosts typically over-cater to impress friends and family, with more than half (49.2%) putting on a larger than necessary spread.

Salad leaves, burger rolls, hot dog buns, coleslaw and potato salad are the top five food items most likely to be wasted during barbecue season, the research found, amounting to £36.47 worth of food waste at each event. The total does not include drink.

Salad days soon over: consumers throw away 40% of bagged leaves

Britons throw away 40% of the bagged salad they buy every year, according to the latest data, with 37,000 tonnes – the equivalent of 178m bags – going uneaten every year.

UK throwing away £13bn of food each year, latest figures show

An estimated 7.3m tonnes of household food waste was thrown away in 2015 – up from 7m tonnes in 2012.

UK households binned £13bn worth of food in 2015 that could have been eaten, according to new figures which suggest that progress in reducing the national food waste mountain has stalled.

Of the food thrown away, 4.4m tonnes was deemed to be “avoidable” waste that was edible at some point before it was put in the bin or food waste caddy – such as bread that goes mouldy – compared with 4.2m tonnes in 2012. The rest were scraps that could not be eaten such as meat bones, eggshells, tea bags, coffee grounds, apple cores and fruit and vegetable peelings.

That meant the average UK household wasted £470 worth of food, which went in the bin when it could have been eaten. The avoidable food waste generated 19m tonnes of greenhouse gases over its lifetime – and preventing that pollution would be equivalent to taking one in four cars off UK roads, Wrap said.

Here are some possible questions:
  1. How much does one potato cost?
  2. How much does a kg of food cost?
  3. According to the figures in the first article, how many families are there in the UK?
  4. What errors/inconsistencies are there in the articles?
  5. How do the figures in the BBQ article fit together? 
  6. How much does one bag of salad weigh?
  7. How many bags of salad are bought each year?


Sunday, 5 November 2017

Quibans 72: Academy football

From BBC Sport.  There is some Fermi estimation here alongside the usual skills.

Academy football: Zac Brunt case
There are an estimated 3,000 children aged between nine and 16 in Premier League academies, with thousands more throughout the Football League.

"Unless you're the next [Cristiano] Ronaldo, clubs don't want to pay £120,000 for a 15-year-old."  Aged 15, Zac Brunt has been part of academies at Aston Villa, Manchester City, Atletico Madrid, and most recently Derby.  He spent the past two years with the Championship club's elite academy on what is commonly known as an Elite Player Performance Plan (EPPP) - designed to bring the best young players, the best coaches and the best environments together at an early age.

"I felt like I wasn't getting anywhere at Derby," Brunt told the BBC. "Other clubs are interested but the fee is so big. For two years work, have I cost Derby County £120,000? Probably not.  "I think this could be the end of my career. I can't go anywhere else apart from semi-professional - the highest level I can go - unless a professional team buys me out of this clause."

The Premier League and the English Football League (EFL) said the "vast majority" of young players moving between academies have compensation waived.

Why so much money?
Compensation formula for academy players when joining another club
Age group of player
Category of club academy leaving
Applicable annual fixed fee - new club to pay
U9 to U11
All Categories
U12 to U16
Category 1
U12 to U16
Category 2
U12 to U16
Category 3

The £120,000 compensation fee that any other academy must pay Derby to sign Brunt is worked out from his three-year registration at their category one academy (£40,000 + £40,000 + £40,000).

Brunt says he understands the need for a rule to protect clubs' investments, but added: "I know a few boys who have been absolutely ruined by this rule and they had to stop playing football and go and play non-league or something like that because they just can't get in anywhere.

Brunt's dad Glen says his son has been for trials with other top clubs, but the compensation fee is putting them off - comparing it to the £7,000 Derby paid Manchester City to sign the youngster themselves.

So is this an unusual case?
The Premier League and the EFL say so.  For example, from about 3,000 Premier League academy players last season, 210 left a club early and, of those, 182 (##%) had compensation rights waived. That percentage has remained above 80% for the past three years.

  1. What inconsistencies are there in the article?
  2. How many children are there in each age group in each club in the premier league?
  3. If Derby get £120,000 what will their percentage profit be?
  4. What percentage of players leave a club early?
  5. How many players from each age group leave each team early each year on average?
  6. How many of these players will play premier league football?

  1. He has been at Derby for two years, but will apparently cost other clubs the equivalent of three years of payments (3 x £40,000).    Why did Derby pay £7000 for the player?  Where does that fit into the structure?
  2. Slightly strangely, “Under 9s” means players who are under 9 years old at the start of the season.  By the end of the season it might be the case that all the players are actually 9 years old.  The phrase at the start of the article: “there are 3000 players aged between 9 and 16” might refer to 7 year groups or to 8.  There are 20 clubs in the premier league.  This gives about 20 players in each year group at each club (3000 / (20 x 7.5) ).
  3. 120,000 / 7000 = 17.14   Subtract 1 to leave the profit and then express as a percentage: 1614%
  4. 210 / 3000 = 7%.  [Also: the hashed out figure is 87%.]
  5. 210 leave 20 clubs, which is 10.5 from each club.  Presumably we shouldn’t include the oldest year group (“leave the clubs early”), so divide this by 6 or 7.  It’s just under 2 per year group at each club.
  6. This is interesting (and hard!).  If a club has a senior playing staff of about 30, aged between 18 and 33 then about two of them will retire each year.  Some of the other players will move abroad or to lower-league teams, but some will be replaced with players from abroad or from lower leagues.  Maybe 2 per year from the youth team making it through to each premier league squad is reasonable.  So that’s about 10% of those who are in the top year group.

Friday, 20 October 2017

Quibans 71: I’d walk a million miles for one of your goals

Apparently (thanks to Scott for the heads-up), Scottish football fans sing “I’d walk a million miles for one of your goals”.  [Link]  

What questions could we ask and answer?  (My suggestions are below.)
How many times around Scotland would that be?
How many trips from Land’s End to John O’Groats?
How long would it take you?  (What is a reasonable number of miles to walk in a day?)

According to Wikipedia, the mainland coastline of Scotland is 6160 miles and the border with England is 96 miles.  This gives 6256 miles in total and 160 laps will be necessary to get over 1 million miles.
Land’s End to John O’Goats is 874 miles – so that’s 1145 journeys to get over a million miles.  (One journey being counted as one direction only.)

If you walk 30 miles a day then it will take over 91 years to do it.  What age would you need to be to start walking this sort of distance, though?

Monday, 18 September 2017

Quibans 70: Commuting by train

As part of an article about commuting an article from the Daily Telegraph includes an information box.

It gives numbers and what they stand for.  Match them up.

700 million

100 million

2.99 million



Journeys made by season ticket holders out of Waterloo station alone

Average amount of weekday morning trains at peak times that were overcrowded

Number of people commuting more than two hours per day in 2014, an increase of 72pc in 10 years

The number of journeys made by season ticket holders across the UK in 2014-15.

Number of people forced to stand every morning on peak trains into the capital - an increase of 19,000 in a year

Here is the box in full:


1) What percentage of journeys that were made in 2014-15 involve Waterloo station?

2) How many season ticket holders are there?

3) How many people commuted for more than two hours per day ten years previously?

4) What percentage of season ticket holders travelled longer than 2 hours?

5) By what percentage did the number of people forced to stand on trains into London rise by?

6) If that percentage increase continues, how long will it be before half a million people are standing?  Is this realistic?


1) 100/700 = 14.2857...%  Given that the two numbers are clearly not exact it would be appropriate to give the percentage as 14%.

2) This is difficult!  700 million journeys per day.  If a passenger takes more than one train does that count as more than one journey?  How many days per year will they travel?  48 working weeks x 5 days = 240 work-days per year, which will be at least 480 journeys (there and back) per person.  Some will take more than one train so let's call that 500 journeys per person on average.  700 million / 500 = 1.4 million commuters.

3) 2.99 million is 172% of the 10-years-ago value.  Back then it was 2.99 million / 1.72 = 1.74 million

4) 139000 out of 1.4 million = 9.9%.  Call it 10%

5)  In the previous year 120,000 people stood on their train and it rose by 19,000.  This is a 15.8% rise (16%)

6) We need 120 * 1.16^n > 500.  Then we need to subtract 1 from n.  Use a spreadsheet to see that n=10 is the first time 500 is breached.  So a further 9 years will be required.  This involves major extrapolation, so is unlikely to be accurate.

Sunday, 17 September 2017

Quibans 69: QR code of trees

From BBC News:

Chinese maze: Village makes giant tech code from trees

At first glance, it could be the courtly maze of an English country manor - albeit with some rather large gaps.

But a tech-savvy eye will instantly see the green design for what it is - a massive QR code.  These high-tech barcodes are hugely popular in China as a way to make cashless payments on a smartphone.

Xilinshui village, in the northern Hebei province, has created one from trees in a bid to raise its profile.  The design was made from 130,000 Chinese junipers, and can be scanned from above using a phone or tablet.

It is not clear how high above the trees you would have to be to scan it - or how you might get there - but visitors who successfully capture the code will be connected to the village's tourism account on WeChat, a Chinese social media site.

The vast design measures 227m (744ft) along each side, and the trees are between 80cm and 2.5m in height, the South China Morning Post reports.  Xilinshui was named "the most beautiful village in Hebei" in 2015, and received a 1.1 million yuan ($168,000; £124,00) development grant from the province.

Some possible questions:

1) What typo is there in the article?
2) You can see this as being made up of square pixels.  What is the side-length of each pixel?
3) How many juniper trees are there in each pixel?
4) What is the conversion factor between metres and feet?
5) Convert the heights of the trees to feet and inches.
6) What are the conversion factors between the currencies?
7) If they spent all of the development grant money on tress how much was each one?
8) How long might it have taken to plant all of the trees?

Some answers:

1) Typo: “($168,000; £124,00) development grant” – it looks as if a zero is missing from the sterling figure.
2) Side-length of each pixel: I count 37 pixels along each edge, but if the empty border is included then it is 39 by 39.  227 metres divided by 37 is 6.1m, whereas 227m divided by 39 is 5.8m.  Let’s say 6m.
3) Number of trees in a pixel: I counted part of it and then scaled up – I got about 650 tree-filled pixels.  This means there are, on average, 200 trees per pixel.
4) What is the conversion factor between metres and feet?  Remember there are 12 inches in a foot.  3.278 feet is 3 feet 3 inches.
5) 80cm is 2 feet 7 inches.  2.5m is 8 feet 2 inches.
6) Convert currencies: $1 = 6.55 yuan.  £1 = $1.35 £1 = 8.87 yuan.
7) Cost of a tree:  8.46 yuan.  About 95 pence.
8) How long to plant them:  If we assume one minute per tree (because they were very small when planted) and an 8 hour day, five days per week, then it would take one person 54 weeks to plant the trees.  Essentially it is a year.  If we have two people working on this then we can divide the time required.  If it takes longer than a minute to plant a tree (which is likely!) then we will need to multiply.

Thursday, 17 August 2017

Quibans 68: Human Chain

 from the Daily Telegraph:

Beachgoers form incredible human chain to save drowning family  

This is the incredible moment strangers on a beach formed a human chain to save a drowning family caught in a riptide in the Gulf of Mexico.
Dozens of beachgoers, including some who couldn’t swim, joined together and linked arms to help nine people, including two young children, swept away by the powerful offshore current.
Around 70-80 people were involved in the dramatic rescue effort on a busy Panama City Beach in Florida on July 8.
Jessica Simmons, a strong swimmer who jumped in to help, along with her husband, initially assumed there was a shark in the water before she realised people were drowning. 
“Some people started gathering people on the beach to form a human chain,” she said. 

How far out to sea were the family?  Give an upper bound and a lower bound.

Sunday, 11 June 2017

Quibans 67: General Election graphs

Here is a sprinkling of infographics and data about the election from a number of different sources (listed below).  These could all be used as a full lesson, or a few could be selected.  (NB: my brief answers follow the questions, so it may be sensible/necessary to copy the images to a file before displaying them.)

Voting by demographic:

It is obvious what most of the categories mean.  AB, C1, C2, DE might be unfamiliar.  They are a way to describe different groups based on their type of employment.  See here.

What are the good things about this infographic?
What are the problems?
What does it show us?

It shows the percentages as well as the party colours.
The numbers are not easy to read.  It is easier to pick out the blue proportion each time and to compare these across the different demographics because they are aligned to the left.  This is harder with the other colours.
It shows us that older people are more likely to vote Conservative.  (Lots of other things too.)

Question: What are these two diagrams?  What do they show?

Answer: The left is a map that shows the colour of each constituency after the 2017 election.  the right shows each constituency the same size and has them in roughly the right place relative to each other.  The left-hand one looks overwhelmingly blue, with the yellow/orange parts being bigger than the red.  The right-hand one clearly has rather a lot of red involved. This suggests that Labour supporters are overwhelmingly from cities (where the area is small compared to the population) whereas Conservative support comes from rural areas.

The next two graphs come from two different newspapers.
What is the same/different about them?  Any other comments?

(NB: check the axes!)

What do the columns mean?  What is the link between the number of seats and the share of the vote?

We might expect that a party that gets 42.45% of the vote would get 42.45% of the seats.  Why is this not the case?
Is that unfair?

This could be worked out using a spreadsheet:

Party Percentage Seats Seats shared using % How many extra seats?
Conservative 42.45 318 276 42
Labour 39.99 262 260 2
SNP 3.04 35 20 15
LibDem 7.37 12 48 -36
DUP 0.91 10 6 4
Sinn Fein 0.74 7 5 2
Plaid Cymru 0.51 4 3 1
Green 1.63 1 11 -10
Ind 0.45 1 3 -2
UUP 0.26 0 2 -2
SDLP 0.3 0 2 -2
UKIP 1.84 0 12 -12
Other 0.52 0 3 -3
  100.01 650    

The 4th column shows what 42.45% of 650 seats is.  The final column shows that the Conservatives got an additional 42 seats over and above that amount.  This is a result of the 'first-past-the-post' system we use in this country whereby each constituency is sorted out separately.  The Green Party got a few votes in many constituencies. Other countries (including elections for the Scottish Parliament) have voting systems that are more proportional than that.

What do these graphs tell us?  Are their titles accurate?


Answer:  They do seem to be accurate.

What is going on here?

Answer: This is difficult to interpret.  Are these the changes in the percentage values, or are they the percentage change in the percentages?  What else can you see in these?

Guardian, via:
Financial Times, via:

Quibans 73: Food waste

Here are excerpts from four Guardian articles, all from 2017. The original headlines are shown in bold. Nearly half of all fresh potatoes t...