A tough question

A student asked me a difficult question the other day.

I’m normally pretty confident with my subject knowledge, and am rarely stumped when quizzed out of the blue. Sometimes a tricky question from Further Maths, or a more esoteric A level problem may leave me scratching my head for a minute or two. Worst case scenario, I may need to ponder the problem for ten minutes in the calm, peace and quite of break time or lunch time, when I can focus on it without distraction, but, typically, I’ll get there in the end and give the pupil the answer they were seeking.

But not this time. As soon as the question was asked, I knew I could not give a definitive answer.

I tried flanneling and digressing, diverting and avoiding, but this Year 11 student was having none of it (perhaps a future career as a “Paxman” on Newsnight beckons?)

In the end I hand to come clean, I had to give an answer, so I did, but I still feel uneasy about it as I’m not sure I’d give the same answer today, as I did then (but I might  do.)

So what was this question that floored me?

Sir, what is your best, ever, music track?

And you can’t answer that question as it constantly changes (but if you want to know what answer I gave when my resistance crumbled, then keep reading.)

I was reminded of this exchange as I’ve just seen my Spotify data for the year.

We live in the age of Big Data and understanding this, how its used and how it shapes our lives is an important lesson for us all to learn.

Fortunately, I love data and I didn’t just stop with what Spotify told me in their glossy end of year review of me, and my listening habits.

I was able to work out that it costs me less than a penny a minute to listen to Spotify, over the year I spent about 50p an hour listening to my music through their streaming site.

Good value? I think it is, I love my music and having so much on tap makes that a price I’m happy to pay (and, as I’m on a family membership, the cost per hour for all four of us in the household is significantly less.)

But the important thing is is that I was able to calculate that cost, and then decide if it was good value for money for me. Many of your students will have received a similar review from Spotify – why not get them to calculate what it costs them (or, more likely, their parents) for each hour they use the service?  The maths is pretty simple, but the process and analysis is so important. I suspect that if I did a similar calculation for my gym membership it may not be such good value for money. Netflix – how much do a pay for each hour I watch?

Still with me? That’s probably because you want to know my “favourite track”.

Well this are my favourites based on my Spotify listening:

But how did I answer the question?

Well, the band in question – The Jam – is in the list above, but not the song.

So what is my all time favourite track? With the caveat that it changes, I can reveal it as “Thick as Thieves” by The Jam.

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Deaths due to terrorism in the UK

I came across the graph above and I was immediately struck by the stories it tells by forcing you, the reader, to ask the obvious questions.

Clearly something happened in the 1990’s.

The peace process was begun in Northern Ireland, culminating in the Good Friday Agreement of 1998. Surely this graph alone is enough to convince anyone of the importance and historical significance of the Good Friday Agreement? Why would anyone do anything, anything, to jeopardise its continued success? If anyone should need any convincing that we shouldn’t, we mustn’t, return to a hard border on the island of Ireland, then surely this graph must be all it takes.

86% of the deaths between 1970 and 1990 were in Northern Ireland

1988 – includes 271 deaths due to the Lockerbie bombing, when Pan Am flight 103 from Frankfurt to Detroit, via London & New York, was destroyed in the air over the Scottish town of Lockerbie by a terrorist bomb.

2005? The tragedy of the London bombings, or 7/7

A simple, sobering graph, but one that deserves – demands – to be viewed.

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The Aeroplane Seating Problem

As ever, the publication last week of A level results, and the imminent release of GCSE results later this week, signal the beginning of the end of the wonderful long summer holidays.

I hope you’ve had a fantastic time and, possibly, enjoyed the delights of foreign travel. If you did, I doubt you flew with an airline with such a relaxed seating plan as the one in the problem below …

On this particular flight, MathAir 314, there are 100 hundred passenger seats, and 100 passengers.

The first passenger to board has lost their boarding pass and doesn’t know their seat number. “No worries” declares the helpful steward, sit wherever you like.

The next (and all subsequent passengers) does have her boarding pass – if her seat is free, she sits in that seat. If it is occupied, the helpful steward allows them to chose any unoccupied seat they wish. This continues until all 100 seats are filled by the 100 passengers and the jet departs for its destination, Angle C (Anglesey – geddit?)

The question is:

What is the probability that passenger 100 gets to sit in their own allocated seat?

I’m indebted to Zoe Griffiths, @ZoeLGriffiths for this problem and you can see her video introducing the problem and, more importantly, her solution in the video below. But before you watch it, have a go at solving the problem yourself first. (You can start the video and the pause it after 1min 30 sec to see her intro to the problem.)

How might I use this problem? I might introduce it to a class towards the end of a lesson, and ask them to go away and think about it, reporting back with possible solutions, or even just approaches to a solution, next lesson.

Or I might offer the problem at the end of a weekly department meeting, inviting colleague to think about it before next week’s meeting. PE teachers regularly play their sports for fun, music teachers their instruments, its important for maths teachers to remain engaged with the subject and “do” some maths from time to time.

So, here’s the video with the solution, but give the problem some thought before you hit play.

 

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Were the refs more lenient on the hosts in Russia 2018?

We may be on the eve of the new domestic football season, but before we consign the World Cup, Russia 2018, to history, I just want to share this plot with you.

It compares the fouls committed per game by a team, and the number of yellow cards received.

By eye, there does appear to be some correlation between the number of fouls committed by a team and the amount of yellow cards they received. This would be expected.

The hosts, Russia, do appear to be an outlier – the third most fouling nation, yet their card count was low.

This could be for a number of reasons – e.g. if many of the fouls they commit were for, say, offside, you wouldn’t expect them to be receiving yellow cards for those offences. But everyone loves a good conspiracy theory – perhaps the refs, either intentionally or subconsciously, were a little more reluctant to flash their cards for the home team …

It prompts an interesting question to explore for the forthcoming season: do away teams get carded more frequently than home teams?

Many thanks to Answer Miner  for creating and sharing the plot. You can see his original tweet with it here.

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Saints or Sinners?

The football may be over, but the fun never stops!

There is plenty of data on the recent Russia 2018 World Cup to be found on the Official Fifa site

Using their statistics, I have compared the number of fouls committed versus the number of fouls suffered and plotted the scatter graph above.  Fouls committed are on the x axis, fouls suffered on the y. The line is a (computer generated) line of best fit using linear regression.

The greater the distance above the line, the more “saintly” we can say a team was – more fouled against than fouling; those below the line were the “sinners” of the tournament.

Using my criteria, we can say that, despite not coming home with the trophy, England were the Saints of the World Cup!

(A note of caution, however. As ever with data, we must always consider its validity.  Despite this data coming from the official FIFA website, it has a total of 1734 fouls committed,  but only 1642 fouls suffered – at the time of writing I can’t reconcile the difference.)

UPDATE

A few readers have (correctly) pointed out that the plot is skewed as not all teams play the same amount of games: one would expect France, Croatia, Belgium and England to all be towards the right of the graph as they played more games than other teams.

So I went back to the data produced a plot for fouls committed per game v fouls suffered per game. You can see the plot below. I think we can safely say those above the line were the saints, those below the sinners.

 

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