Thursday, 15 February 2018

Quibans 81: Good graph, bad graph

Here are two data representations from the same Daily Telegraph article about shootings in schools in the USA.


My thoughts are below.








I like the first one.  This is very clear and shows when incidents occurred.  There seem to be several weeks where lots of incidents happened.
February was less incident-filled than January.  (NB this graph was published 15 Feb.)
There are some confusing things: Was 15 Jan a school-day?  There was an incident on a Saturday. What does 'incident' mean?  On the black-cross days - were there 2 incidents or more than that.

In the second graph things seem completely backwards!  Here a smaller bar means the mass-shootings were closer together, which doesn't seem obvious.  Is there a better way to show this? 
Does it matter that the groups of years are not the same size? 

Lots to talk about here!


Monday, 5 February 2018

Quibans 80: Manchester Disunited

Man Utd face pressure to end 'grotesque' failure to pay Living Wage while Alexis Sanchez earns £600k-a-week


Manchester United will come under major pressure on Thursday to end their “grotesque” failure to pay all workers there the “real” Living Wage after making Alexis Sanchez the highest-paid player in Premier League history during the transfer window.

In November both United and Manchester City faced political pressure to join Liverpool in pledging to ensure everyone who carried out work on their behalf would receive at least £8.75 per hour.

Led by civil society alliance Manchester Citizens, part of campaigning charity Citizens UK, Thursday’s action is accompanied by a release headlined ‘Manchester Divided’, which proclaims Sanchez’s signing has further exposed “a grotesque tale of halves”, in which five of the highest-paid players in the Premier League play for United or City - including Paul Pogba, Kevin De Bruyne, Romelu Lukaku and Zlatan Ibrahimovic - while “low-paid staff at the Theatre of Dreams are facing a real nightmare to meet the real cost of living”.

It also claims Sanchez makes almost as much during one half of football than the annual salary of some cleaning, catering and security staff who work at Old Trafford (£14,625), that it would take someone on the minimum wage 41 years to earn the £600,000 the Chilean takes home each week, and that his agent’s reported £15 million fee would be enough to fund Living Wage pay rises of almost £2,500 for 6,100 low-paid workers.

One such worker at Old Trafford, who did not want to be named for fear of reprisals, said: “We all share the same employer and it would be great if the club could think about all workers’ wages, from football stars to stadium cleaners and caterers”.


1) How much does Sanchez earn per year?

2) Assuming he pays tax at 45% on his earnings, how much is his weekly take-home pay?

3) If the stadium workers earn £8.50 per hour, how many hours per week do they work?

4) Example the claims in the penultimate paragraph. Are they true?

5) If he drops a 50p coin, is it worth his while to bend down and pick it up?


1) £600,000 x 52 = £31.2 million

2) £330,000 (while he will have a tax-free allowance of about £10,000 and a lower rate for the next chunk of his salary, this is negligible).

3) This is about 36 hours per week, assuming they work for 48 weeks per year. There is something a little strange here, in that presumably many more staff are needed during a match than on other days. Presumably many of the workers are therefore part-time.

4) In one half of football Sanchez makes £14,625? This works if he is considered to be ‘working’ for 30 hours per week throughout the year.

41 year? Yes.

Agent’s fee of £15 million? Yes

5) If you divide his salary up across the week it comes to about 99p per second (even for the time he is asleep). In the ~2 seconds it would take for him to lean down to pick up a 50p coin he will have earned 4 times that!


Saturday, 27 January 2018

Quibans 79: Nutella Riots

From the BBC:

Nutella 'riots' spread across French supermarkets

A discount on Nutella has led to violent scenes in a chain of French supermarkets, as shoppers jostled to grab a bargain on the sweet spread.
Intermarché supermarkets offered a 70% discount on Nutella, bringing the price down from €### (£3.90) to €1.40.
But police were called when people began fighting and pushing one another.
Some 365 million kilos of Nutella, a hazelnut chocolate spread, is consumed every year in 160 countries around the world.

Here is information about Nutella from the Tesco website:
  • Pack size: 750g


Sugar, Palm Oil, Hazelnuts (13%), Fat-Reduced Cocoa (7.4%), Skimmed Milk Powder (6.6%), Whey Powder (Milk), Emulsifier: Lecithin (Soya), Vanillin

50 Portions per jar = 50 x 15g

What can we work out?  Some ideas are below.





Q1)  Work out the missing number
Q2)  What is the exchange rate?
Q3)  How many portions are sold each year?
Q4)  How many tonnes of Nutella are sold each year?
Q5)  How many kg of hazelnuts/coca/milk are used each year?
Q6)  Ingredients are listed in order (highest amount to lowest).  What is the smallest percentage of sugar there could be?

Q1)  Intermarché supermarkets offered a 70% discount on Nutella, bringing the price down from €4.50 (£3.90) to €1.40.
This is interesting because if you do 1.40/0.3 you get 4.67
There has been some rounding going on!  The actual discount is 68.9%
Q2)  £1 = €1.15
Q3)  365 million kg divided by 15g = 24 billion servings.  (That's more than 3 servings per person on the planet)
Q4)  365,000 tonnes  - that's 1000 tonnes per day!
Q5)  Hazelnuts - 47,000 tonnes, Coca - 27,000 tonnes, Milk powder - 24,000 tonnes
Q6)  If the smallest three ingredients are the biggest they can possibly be then they will each be 6.6% and the total of everything other than sugar and palm oil is 46.8%.  The smallest the sugar can be is half of what remains, which is 26.6%.  In reality this is likely to be a big underestimate.


Tuesday, 16 January 2018

Quibans 78: Expensive wine

In my Spanish class we read a newspaper article about the most expensive wine in the world.  Here is my translation of part of that article:

This is the most expensive wine in the world and it’s made in Spain.
Each bottle of AurumRed ‘gold series’ costs €25,000.  Hilario García produces 300 of these bottles per season, of which he sells 150 immediately and reserves the rest for repeat clients, and there are some of them.
The cellar also produces 6,000 bottles per year of the ‘silver series’, at €2,200 per piece and 3,000 bottles of sauvignon blanc, which is much more accessible at €30.

1)      What is the average cost of a bottle of wine from this vineyard?
2)      Comment on the usefulness of this answer

Translation: MD

Original text:
Así es el vino más caro del mundo, que se hace en España
Cada botella de AurumRed serie oro cuesta 25.000 euros.  Hilario García produce al año 300 de estas botellas, de las que comercializa 150 por temporada, y reserva el resto para los clientes que quieren repetir, que los hay.

De la bodega salen también 6.000 botellas al año de la serie plata, a 2.200 euros la pieza, y 3.000 de sauvignon blanc mucho más asequibles, a unos 30 euros.

Wednesday, 10 January 2018

Quibans 77: Brussels Sprouts at Lidl

On the radio this morning they reported:
Lidl supermarket said it had record UK sales in December, with a rise of 16% on the same period in 2016.
Customers bought about #### tonnes of Brussels sprouts.

I told my class this and said that the first digit of the number of tonnes of sprouts was a 6.  They then worked out a likely number.

What they did is below.
Here is one solution.  Others were shared too.
  • Assumption: 1 sprout weighs about 10g.  We know that 1 tonne = 1 million g, so this is 1/100,000 of a tonne.
  • Assumption: Each person in the country has 5 sprouts at Christmas.
  • Assumption: There are 64 million people in the country.

Multiplying these gives a total sale of 3200 tonnes of sprouts.
Some people buy these from supermarkets (and there are lots of these: Tesco, Sainsburys, Morrisons, Asda, Waitrose, Lidl, Aldi, M&S, Co-Op, Spar), some from local shops and others will grow their own.
Those studying business studies predicted that Lidl might have approx 10% market-share.  
We assumed that this meant they sold 10% of the sprouts too (this is an assumption we need to make.  For example, Iceland (the shop) has more frozen food, so their market share couldn't be used to predict sales for fresh produce).
Lidl would therefore sell 320 tonnes of sprouts.

The next part is the thing I found particularly interesting.  The students pointed out that 320 tonnes was almost exactly midway between 60 tonnes and 600 tonnes.  The halfway point is 330 tonnes.  The students were aware that in an answer as full of estimates as this they couldn't say that their 320 is less than 330 (which is right and sensible), but they were unclear whether they should round up to 600 or round down to 60.

After discussion they were happy with the idea that we usually think in a multiplicative way about our errors in a question like this (so we predicted 5 sprouts per person, but it could have easily been double that).  To get to 600 you multiply by a number less than 2, whereas if you divide by 5 you haven't reached 60.  They decided on 600 tonnes as the answer.

Here is the start of the story (from the BBC News site):
Lidl supermarket said it had record UK sales in December, with a rise of 16% on the same period in 2016.
Customers bought about 600 tonnes of Brussels sprouts

Sunday, 31 December 2017

Quibans 76: Away matches

During the Christmas period (the weekend before Christmas, up until just into the New Year) the Premier League football teams play four games.  BBC Sport website had this as a headline:

Premier League festive fixtures: Which clubs have toughest schedule?

As part of this they looked at how far supporters of each club would travel if they attended all four games.  (Distances are measured by road from the stadium of their own club.) 

Q1) Across the whole season, which team's supporters would you expect to travel the furthest?  Which would travel the least?

Here are the teams and a rough indication of where they are
Arsenal   (London)
Bournemouth   (South coast)
Brighton and Hove Albion   (South coast)
Burnley   (North west)
Chelsea   (London)
Crystal Palace   (London)
Everton   (North west)
Huddersfield Town   (North west)
Leicester City   (Midlands)
Liverpool   (North west)
Manchester City   (North west)
Manchester United   (North west)
Newcastle United   (North east)
Southampton   (South coast)
Stoke City   (Midlands)
Swansea City   (South Wales)
Tottenham Hotspur   (London)
Watford   (London)
West Bromwich Albion   (Midlands)
West Ham United   (London)

Here is a map of the teams (taken from, with the teams highlighted in blue). 

Q2)  Do you want to change your answers?  (NB: Liverpool and Everton are so close together that they appear as a single dot here.)

In the article this graph was included:

Q3)  What sort of correlation do you think there is between the distance travelled during the Christmas period and that travelled during the whole season?  Can you predict the pmcc?

Here are the figures (taken from a Talksport article, from awadayplanner and from the BBC).  The spreadsheet can be downloaded here.


It might initially appear that all teams will travel the same distance to play each other, but further reflection suggests that teams that are closer to the middle of the country are likely to travel the least.
There are several ways to think about this.  There are six teams in London.  Their journeys to play each other will be quite short, but for Newcastle to play each of the six London teams they will need to make six long journeys.

One way to convince yourself that clubs on the periphery are likely to travel furthest (Eg Newcastle, Swansea, Burnley, Brighton) is to go to ridiculous extremes.  If Pluto United joined the premier league then for one game each season the other 19 clubs would travel once to Pluto.  But the fans of Pluto United would have to travel to Earth 19 times to play each of their away games.

In all of this we are making the assumption that each match is a self-contained trip.  It might be possible for Newcastle fans to make a single trip to London and to stay there for all of the London matches, but in practice this will mean living in London for the season, because football teams rarely play two matches in three days and usually (roughly) alternate between playing a match at home and then one away.

The table for Q3 shows the clubs in order.  I had predicted that Newcastle and Swansea would be the two clubs with the furthest journeys and that a north London club would have the shortest journey in total.

Burnley were particularly fortunate with their festive travel distances.  Tottenham Hotspur were a bit hard done by. 
The pmcc is 0.52 - indicating a weak positive correlation.


Wednesday, 20 December 2017

Quibans 75: Don't Panic!

This story appeared in most newspapers.  The Sun put it like this:

200 litres every hour!  Clearly letting in water isn't ideal for a ship, but is 200 litres a lot?

How long before it will sink?

Some data here (from the Daily Telegraph) might help:

Some thoughts/answers:
I googled the capacity of a standard bath-tub.  It appears that 120 litres or 150 litres are fairly common capacities.
To put this into perspective: it's letting in about one and a third bath-tubs of water per hour.  That doesn't seem very much!

A length of 920 feet, beam of 230 feet and draught of 36 feet are given in the Daily Telegraph graphic.  I assume that 'beam' means the width of the ship and that the 'draught' is the amount of ship under the waterline.  There is a lot of aircraft carrier above the waterline, but if we find the rough volume of ship underwater (treating it a cuboid) then we would get 920*0.3 * 230*0.3 * 36*0.3, which is about 200,000 cubic metres.  That's 200 million litres.

At 200 litres per hour that is a nice round million hours before the part currently below the waterline to fill with water.  It will take just over 100 years for this to happen.  So if left untreated, if it still exists in a hundred years, if no-one uses a pump, and if the navy runs out of buckets for bailing purposes, then the ship will probably be in trouble early in the 22nd century.


Quibans 81: Good graph, bad graph

Here are two data representations from the same Daily Telegraph article about shootings in schools in the USA. Comments? My thou...