Wednesday, 18 March 2020

Quibans 95: The 50p at 50

From the Guardian.

50p at 50: how Britons' living costs have changed since 1969

The 50p coin entered circulation on 14 October 1969, in the run-up to D-Day on 15 February 1971, when the UK finally abandoned shillings and pence and moved to a decimal currency.

The 50p coin was worth a lot then – indeed, more than any coin in circulation now. In real terms it was worth the equivalent of just over £8. Fifty years on, especially after rampaging inflation in the 1970s, the 50p is a shadow of its former self – it has shrunk in size and weight, but above all in value.

But what do these figures mean in real terms? Inflation since 1969 has been an astonishing ## %, with the fast-rising “cost of living” already a major headache for the government at the end of the 1960s.

What is extraordinary about the wages data from the late 1960s is the huge gap between men and women. The ONS New Earnings Survey for 1970 shows that the average full-time male worker was paid £30 a week, while a female full-time worker earned just £16.30. Annually, that worked out at £ ## for men, which is equal to £24,050 today, but only £ ## for women, equal to £ ## today.

A look through the Guardian’s classified job adverts on the day the 50p was launched gives a snapshot of what real jobs paid. The Open University, which had just been established, was hiring professors at £3,780 a year (equal to £ ## today), lecturers on a range of £ ## to £ ## (£20,153-£47,147), and secretaries on £ ## -£1,068 (£12,506-£ ##).

The Open University is still hiring – and its adverts suggest that real pay for academics has barely edged ahead in 50 years. It currently has an advert for a professor of economics on a range of £67,700-£75,800, while it pays lecturers £33,000 to £49,000. But the secretary job pays lots more in today’s money, with the OU advertising a role at £23,000 to £26,000.


Work out the numbers that have been replaced by ## symbols.

What is the real-terms increase of salary for Professors, Lecturers and Secretaries (using the top of the pay scale each time)?


Inflation since 1969 has been an astonishing 1,554%

The ONS New Earnings Survey for 1970 shows that the average full-time male worker was paid £30 a week, while a female full-time worker earned just £16.30. Annually, that worked out at £1,560 for men, which is equal to £24,050 today, but only £847.60 for women, equal to £13,068 today.

The Open University, which had just been established, was hiring professors at £3,780 a year (equal to £62,532 today), lecturers on a range of £1,240 to £2,850 (£20,153-£47,147), and secretaries on £756-£1,068 (£12,506-£17,668).
  • Professors: an increase of 21.2%
  • Lecturers: increase of 3.9%
  • Secretaries: increase of 47.2%

Tuesday, 17 March 2020

Quibans 94: Transport in Luxembourg

This is a pre-coronavirus article about public transport in Luxembourg, from the BBC.

Free transport in Luxembourg, but what's the cost?

It has had months of hype and now finally Luxembourg's free public transport has begun.
With a population of only 614,000, it may be one of Europe's smallest countries and the idea is not unprecedented. But the "free mobility" drive has captured the imagination. Buses, trams and trains are now free to ride on and you don't need a ticket.

"The government wants Luxembourg to become a laboratory for mobility," says Mobility Minister Fran├žois Bausch, who points to the grand duchy's fast-rising population, with a rise of 40% in 20 years.

Travelling on transport will be free for residents and visitors alike, except for first-class train passengers.

The price of the project will be the €41m (£35m; $44m) in lost ticket fares, but that will be shouldered by the taxpayer. "Of course, just because I call it free transport doesn't mean nobody pays," said Mr Bausch, who is part of Luxembourg's green party,

The total cost of running the service is more than €500m so the government sees the lost fare revenue as relatively small.

It was not exactly pricey before 29 February. A fare cost €2, and double for a day pass. Many workers have their annual travel pass subsidised in Luxembourg, so few people spend much on transport anyway.

Luxembourg spends more of its economic output on transport that most other European countries, with a reported €600 a year per person.
  1. What was the population of Luxembourg 20 years ago?
  2. What is the exchange rate of the £ to the € , and the £ to the $ ? How can we use these exchange rates to work out the € to the $ ?
  3. Using the cost of running the service and the population, work out how much it costs per person per year. What is strange about this?
  4. Roughly how many public transport journeys are taken each year? How many per week?

  1. 614,000 divided by 1.4 = 438571, so the population was about 440,000
  2. £1 = €1.1714 £1 = $1.2571 This means €1.1714 = $1.2571 , so €1 = $1.0732
  3. €500m divided by 614,000 people is €814 each. Later in the article it says that it spends €600 per person per year on transport. (Presumably this includes roads as well. And airports?)
  4. A ‘day pass’ used to cost €4 and brought in €41 million. Presumably most people made two journeys each day (there and back?). That’s about 10 million journeys. Dividing this by 50 (approx. number of weeks in a year) gives 200,000 journeys per week. If we were to assume that this is 100,000 people then only a small fraction of the population ever use public transport!


Monday, 16 March 2020

Quibans 93 – Royal Families

Quibans 93 – Royal Families
from CNN.

Here's how much Europe's royal families really cost

Question 1:
The UK monarchy is twice as expensive as every other one.  What is potentially misleading about this?

Answer 1:
The population of the UK is massively bigger than that of Monaco!

Question 2:
If we work out the cost per person in each country, where do you think the UK would be?

Answer 2:
Here is the next part of the article:

Question 3:
If we combine these two images, what can we work out?  (Then work it out!)

Answer 3:
We can work out the population of each country.
Here are my workings (with upper and lower bounds included too, perhaps as a talking point):

Question 4:
What else might we need to consider when working out how expensive a Royal Family is?

Answer 4:
There might be lots of other issues.  If palaces are being renovated then that will have a one-off cost.  The number of ‘working royals’ might be different in different countries, so there are different numbers of people being ‘paid’.  More working royals will require more admin support and staff. 
This doesn’t factor in the benefits to a nation of having a monarchy.   This might include the tourism that is attracted.  In the UK system the Queen is the head of state.  If we didn’t have a monarchy then we would need a different person doing that role (such as a president) who would need offices, staff, etc, so some of these costs would still be necessary.

Saturday, 14 March 2020

Quibans 92: Hoarding toilet paper

Quibans 92 – Hoarding toilet paper
From the Daily Telegraph, near the start of the coronavirus pandemic:

Why the UK won't run out of toilet roll
13 March 2020
 As panic over the coronavirus outbreak continues to spread, empty shelves where toilet roll once would have been has become a common sight in many supermarkets. Consumers have been stockpiling the bathroom staple, sparking fears that supermarkets could soon be caught short. However,  there might not be any need to panic.
The UK exported $129m (£103m) of toilet roll in 2019 and exports more than it imports.
“As the world’s 11th-largest exporter of toilet roll, at least if our supply routes shut down, we will be able to keep calm, stop exporting, and carry on,” Dr Rebecca Harding of data firm Coriolis Technologies said.
Ireland accounted for $90.4m or ##% of all UK toilet roll exports in 2019 and is dependent on the UK for 80pc of all toilet roll. Dr Harding said the Irish reliance on the UK for toilet roll is evidence of the importance of borderless trade on the island of Ireland.
  1. What is the exchange rate? 
  2. What percentage of UK exports of toilet roll go to Ireland?
  3. How much does Ireland spend on toilet roll per year?
  4. The population of Ireland is 4.83 million.  How much does each person spend on toilet roll per week?
  5. Four sheets of toilet paper cost about 1p.  How many sheets is that per person per day?

  1. £1 = $1.2524
  2. 70%
  3. 90.4 million divided by 0.8 = $113 million
  4. 45 cents per week
  5. 45 cents is about 36p per week.  Divide by 7 to get the cost per day and multiply by 4 to find the number.  20.5 sheets per day.

Sunday, 15 December 2019

Quibans 91: SPOTY and the Christmas Number 1

'SPOTY' is the annual BBC 'Sports Personality of the Year'. 

This Quibans takes an article from a year ago.  It appears that it is updated each year (and is nonsense every time!).  The versionfor 2019 has been done as a video (but includes the same graphics as in 2018).

Here I present the article a section at a time, with a question after each.  My thoughts and comments appear together at the end.  You may want to give students the address of the webpage and ask them to go through it for themselves.

BBC Sports Personality of the Year: How do you win the main award?

14 December 2018
The BBC Sports Personality of the Year 2018 will be crowned on Sunday but what are the key factors in the make-up of previous winners? From birthplace to facial attributes, we've been analysing the ideal candidate...
The award was first handed out in 1954 and there have been 60 different winners, with Andy Murray the only person to win it on three occasions.

Question 1: This image appears at the end of the article.  It suggests that to win SPOTY you ideally need to do athletics, to have been born in London, to have blue eyes, to be 29 years old and to have had your achievement in August.  Any comments at this stage?

Here is the first image:

Q2)  Why might it not be surprising that there are more Athletics winners than there are from other sports?

Q3)  Why is this unsurprising?

Q4)  Any comments?

Recall the line of text near the start of the article:
The award was first handed out in 1954 and there have been 60 different winners, with Andy Murray the only person to win it on three occasions.
Q6)  Looking at the previous image, what can we work out?

Q7)  Why is this not a surprise?

Q8) So let’s look back at the diagram we started with.  Any further comments?

Here are my answers:

Q2)  There are lots more athletes than there are motor racing drivers and there are lots of sports included under the heading ‘Athletics’.  There are really only 11 England cricketers who might be in with a chance and footballers suffer because people will only vote for national team players and not those from clubs they don’t support, 

Q3)  London is bigger than anywhere else, so it has a larger proportion of the population.

Q4)  What has this got to do with success in sport or with popularity?  Does having green eyes make you less popular?  No.  Does it make you less successful?  No.  And the facial hair is presumably partly to do with fashion.

Q5) If you have blonde hair you are more likely to have blue eyes!  So these two things are linked.

Q6)  There are 65 winners here, so some people have won it twice.

Q7)  Many awards will have been because of events that take place in the summer, such as the Olympic Games (July/August) or Wimbledon (June).  There are most winners from athletics and that is overwhelmingly a summer sport.  Is it also likely that those who win things in Jan/Feb/March are forgotten by the time you get to December and the voting for SPOTY?

Q8) We have said already that athletics and August are likely to be linked and that London is the biggest city in the UK, so is likely to have more people who are born there.  The blue eye colour is interesting: for the men it was equal, but by including the female winners you get blue being the mode.  Clearly, if you are male then this isn’t relevant!  But hold on: vastly more men have won than women, so should that be mentioned here?

Here is a list of the Athletics winners of SPOTY (from Wikipedia):

Of the Athletes, 5 were born in London (Christopher Chataway, Seb Coe, Daley Thompson, Fatima Whitbread and Jonathan Edwards). 

The final four of those appear to have brown eyes, leaving only Christopher Chataway.  He was 23  years old when he won and his big achievement (breaking the 5000m world record) took place in October. 

Chataway meets only the first 3 of the 5 criteria.  Are there any who meet 4 of them?  Jonathan Edwards is the only one of the athletes who makes 4 out of 5.  He was a Triple-Jumper, born in London, was 29 and his world championships win was in August. 

None of the other winners (from any sport) get 4 of the 5. 

So this is an example of where appealing to the averages at every stage doesn’t help us in predicting the winner.

Extension:  Number 1 song at Christmas

This used to be one of the biggest songs of the year.  Many different newspapers carried exactly the same story.  This version comes from the Independent:

Music experts find formula for ‘perfect’ Christmas number one

Music researchers have crunched the numbers on Christmas songs to find the perfect formula for a festive hit.
Experts at a UK music label looked at every Christmas number one from the last 50 years to see what they have in common and determined that the Pet Shop Boys’ 'Always On My Mind' came closest to being the quintessential tune for the holidays.
“I think we’re a long way from an algorithmically-generated Christmas number one,” said Howard Murphy, founder of Ostereo which conducted the research, in a press release accompanying the data.
“But certain characteristics do make a song more likely to resonate with audiences at Christmas,” he added.
For a song to hit the top spot on Christmas Day it needs to be three minutes and 57 seconds, in the key of G major, played at 114 beats-per-minute and performed by a 27-year-old solo artist, according to the research.
Other key trends among the songs analysed were that the majority were ballads, nearly half were cover versions and nearly all were about something other than Christmas.
'Always On My Mind' hits the ideal length and key exactly, as well as being a cover of Elvis’ 1972 hit, but is slightly faster than the formula suggests at 125 bpm and performed by a duo who had an average age of 31.5 when the song hit number one at Christmas 1988.
'Mary’s Boy' by Boney M came a close second, researchers said, with a tempo of 113 bpm, length of four minutes two seconds and a key of F, two semitones lower than G.

Clearly this isn’t a ‘formula’ – they have just averaged the attributes of all the Christmas number one songs over the years.  What types of average have they used for each attribute?  How is this story related to the SPOTY one?


Friday, 12 July 2019

Quibans 90: Goal sizes

This task was test-driven at the recent AMSP Core Maths days (as part of ‘Quibans Live’).  Thanks to those who made suggestions for improvements.

The story appeared in a number of places before the 2019 FIFA Women’s World Cup and there were discussions about whether women should play with smaller goals because women are, on average, shorter than men.  This version is taken from the Daily Telegraph.

'Reducing size of women's goals would not help fight for equality,' says England goalkeeper Karen Bardsley
England goalkeeper Karen Bardsley believes reducing the size of goals in the women's game would jeopardise the fight for equality in football.
Chelsea manager Emma Hayes has suggested the women’s game could be adapted to bridge the ‘physical differences’ between women and their male counterparts.
She suggested smaller goals could stem criticism often directed at female goalkeepers, who are generally of a smaller stature to their male counterparts.
Manchester City goalkeeper Bardsley, about to play in her third World Cup when she will add to her 77 international caps, does not believe narrowing the width between two posts is the way forward.
“My big thing is we need to change how people feel about goalkeeping, I don’t think there is enough respect for the position in the game, whether male or female.
“There is a stigma, that you have to be a certain size, or not very good with your feet, or you have had to go in goal as a last resort.”
How could we explore, using some Core Maths knowledge, whether the goals should be made smaller?

On one level it doesn’t matter.  Football is a relatively low-scoring game (compare it with American Football, basketball, rugby, cricket, etc, where the numbers of points (etc) are very much bigger).  If the goals are bigger than necessary and this results in more goals being scored then this isn’t a big deal.  The goals are the same size for both teams after all.

We could find data for the heights of male and of female goalkeepers and compare them. 
In fact, I think the size of the goal was set in the 1866 version of the laws of the game and according to the BBC the “average height of men has risen by almost 11cm since the mid-19th century”. 
Wikipedia has the current average height of UK men at 175cm and women at 162cm, so if both have increased by about 11cm since the size of the goals was fixed then women are now roughly the same height as men were back then.

Here’s my favourite way to explore this issue:  If the goalposts are too big for women then that presumably means more goals are being scored by women.  Let’s use the number of goals per game from the last two World Cups (Russia 2018 for men and France 2019 for women) and compare the data.

The Google Sheets file has the full data, but here are the relevant parts.  You might want to give the summary data to the class and ask them to work out averages and interpret them.

Before giving it out you might want to ask whether the average number of goals per game will be different in the group stage or the knock-out part of the tournament.

Is this a reasonable set of calculations to do?  Are there ways to improve this?

Those who followed the women’s competition will know that the eventual winners, the USA, beat Thailand 13-0.  This is clearly an outlier, so perhaps we should remove it from the women’s data?

At Quibans Live several people pointed out that if there was extra time in a match then there was more opportunity to score goals (the penalties that follow extra time have not been included here, though that is another avenue that could be explored).  A normal-length match is 90 mins, so extra-time of 30 mins is equivalent to another third of a match.

Here are the results with the 5 extra-time men’s matches and the three extra-time women’s matches included:

Very close indeed!  This data doesn’t suggest the goals should be smaller in the women’s game.

Final thought:
This is clearly relevant to the elite athletes at the last two world cups.  Does it still work for those playing at lower levels?

Friday, 17 May 2019

Quibans 89 – Men vs Women in the European elections 2019

I voted by post earlier in the week.  Some parties had more female candidates than others.  I wondered whether it was the case that across the country certain types of party have more male or female candidates.  Here’s what I did with my Year 12 Core Maths class.

Some background to the electoral system:

Each country in the EU has its own voting system for the European elections.  England is divided into 9 regions and Wales and Scotland are each a region (Northern Ireland has a different system, so I didn’t involve them).  In each region there are a number of seats, ranging from 10 seat for the South East region to 3 seats in the North East.

You don’t vote for an individual but for a party.  Each party has a ‘list’ of candidates for each region.  Last time around in the 7-seat East of England region most parties had seven candidates.  Having worked out that UKIP should get 3 seats, the Conservatives 3 seats and Labour 1 seat (using the D’Hondt method – but that’s not relevant here), the top three candidates from the UKIP list were elected as MEPs, the top three from the Conservative list and top Labour candidate.

What we did:

On a shared Excel file, I had each region on a separate sheet.  I divided these up around the class (some students had a sheet each, others worked as a pair).  First they sorted out whether each candidate was male or female.  This wasn’t always obvious, so they Googled if they weren’t sure.
Then they typed into another sheet the number of female and male candidates for each party.
They had to deal with some issues.  For example, some candidates are standing as ‘independents’, meaning they are not part of a party.  We decided to ignore them.  Some candidates have withdrawn from the election; we removed the ones we knew about.

These are the results, for the parties that are standing in every region:

11% of the UKIP candidates are female, through to Change UK, for whom 57% of the candidates are female.

Is it interesting that the more pro-Brexit parties tend to have more male candidates, while the more pro-Remain parties have roughly equal numbers of men and women?

Better methodology?

But hold on: maybe this doesn’t tell the whole story.  What if the LibDems have the same number of male and female candidates but the top few in each region are all men?  It is extremely unlikely that those further down each list will be elected, so this is important. 

Here is how I intend to deal with that.
The students recorded a list of Male and Female candidates for each party.  Here’s part of that list:

Since the lesson (we will talk about this next week) I have turned that into a set of binary numbers, where F becomes 1 and M becomes 0.

I then turned the binary into a decimal.  This means the first-ranked candidate in each list is worth double the one that follows, which is worth double the one after that, etc.  If there are 5 candidates in a list, the 5th one is worth 1 point, the 4th is worth 2 points, the 3rd gets 4 points, the second gets 8 points and the first is 16 points.  Add up the number of points for the female candidates and then divide by the total (which is 1 + 2 + 4 + 8 + 16 = 31).  That gives a fractional weighted-score for the female candidates in each region.
Then I found the average of these. 

The second column shows this new figure (with the first column showing the previous data):

Not much difference (apart from the Green Party)! 

Final thoughts:

It was good for the students to see a way to carry out this sort of analysis.  
It was good to divide up the work.  I couldn't find an easy way of getting hold of the gender of each candidate, so sharing the workload was a good thing.
We had to decide how to deal with problems (withdrawn candidates).
We had to think about how to do the analysis.

Here are links to my original spreadsheet and the one my class filled in.

If you want your class to use the original version then you will need to save it and share it with them (your IT people in College will be able to help if you haven't done this before).

Quibans 95: The 50p at 50

From the Guardian. 50p at 50: how Britons' living costs have changed since 1969 The 50p coin entered circulation on 14 October 1969, in ...