Singapore Grand Prix qualifying

In Formula 1 the day before each race is a time trial known as ‘qualifying’. The quickest driver in qualifying starts on pole position, with the others being arranged in order behind him.

Lewis Hamilton beat his fellow Mercedes driver Nico Rosberg by 7-thousandths of a second. Here is a tweet from the Mercedes team:

Yes – after a full lap of the circuit the difference between the two drivers’ times was 0.007 seconds!

The Mercedes team then tweeted this:

That is nice, because it leads to a starter activity. What can we work out?

We can work out the average speed of the drivers.

0.335m ÷ 0.007s gives us the speed in m/s.
Multiplying by 3600 will give us the speed in metres per hour.
Dividing by 1600 turns this into mph.

I get the average speed as 108mph. Not bad for a circuit with lots of twists and turns!

Statistical Literacy

Two news articles over the past few days have reminded me of the importance of this.  Both from sources who ought to know better (or whose ideas have been reported in a way that throws them open to interpretation).

First of all, the Stephen Hawking analysis of England’s World Cup chances relied on 45 matches played since 1966.  Other people have already picked holes in this, but I want to add something I haven’t seen mentioned elsewhere, which is that the data that has been used to predict the current England team’s response to matches presumably includes matches played in the early 1970s, before all of the current team were born and before Roy Hodgson was a manager.

Given the way football, fitness, analysis and tactics have changed over the past few years, presumably the early 1970s are as irrelevant to England’s current team and its chances as I am.

The other article, from the BBC, reports a Lancet study about rising levels of obesity.

The article states:

More than half of the world's 671 million obese people live in 10 countries, ranked in order:

• US
• China
• India
• Russia
• Brazil
• Mexico
• Egypt
• Germany
• Pakistan
• Indonesia

Source: The Lancet

Hold on a moment.  China and India have rather big populations.  As does Indonesia.  Let’s have a look at where these countries sit in a list of countries by population. 

	Rank in obesity article	Population rank	Percentage of global population
USA	1	3	4.44%
China	2	1	19%
India	3	2	17.40%
Russia	4	9	2.04%
Brazil	5	5	2.83%
Mexico	6	11	1.67%
Egypt	7	15	1.21%
Germany	8	16	1.13%
Pakistan	9	6	2.60%
Indonesia	10	4	3.45%

Ah – the six most highly populated countries are included on this list.

Adding up the percentages give us just over 55% of the world’s population.  So the article is actually saying “more than half of the world’s obese people live in countries that contain more than half of the world’s people”.  In other words: big deal.

It would be rather more interesting to have some more context for the initial statement in the article:

“The number of people in the world who are obese or overweight has topped 2.1 billion, up from 875 million in 1980, the latest figures published in the Lancet show.”

Estimates (from other sources) suggest that the current population is about 7.17 billion while in 1980 it was 4.4 billion.  This means that the obese population has more than doubled while the general population hasn’t doubled.  Is there a real increase in obesity, or is it, for example, the case that younger people have higher rates of obesity and there are now more younger people than there were 34 years ago?

So: we certainly need more people to be aware of statistical gibberish. 

[The Guardian article does actually appear to understand some of the problems inherent in the “Scientists have found…” type of press release.  It is worth a read.]

Storm in a tea cup

Here's another on my list of "things I wish people wouldn't do".

It starts with exploring something that is largely subjective and then writing a formula to go with it.  The but I don't like is the way it is published, usually featuring the words "mathematicians have created a formula for...", or "scientists have discovered the formula for...".

The worst part of course is that the formulas are often (with a few honourable exceptions) gibberish.

A new low was plumbed with the formula for the "perfect cup of builders' tea".

Have a look at this (taken from the ITV news website):

What could this possibly mean?  Do try and work out what on earth is going on before you read further.

What is the result of this?  What is E ?  How can you multiply that by the sum of q, t and m?

Thankfully the Deccan Herald is on hand to help us out, explaining that:

The final formula for the perfect builders' brew is: 'Perfect cuppa: 2B + 30R + E(m + q + t) + 10W'.
In the formula 2B denotes two minutes of brewing time, 30R is 30 seconds of resting time, E(m + q + t) denotes a big mug, a good quality tea bag and a treat while 10W stands for 10ml milk.

Oh dear.  It sounds as if they played with lots of different variables and tested lots of different ways of making tea, using willing builders as tea-drinking judges.  In the interview I heard with the students on the radio earlier today the journalist expressed surprise that only 10ml of milk was considered optimal, so they have found out something unexpected.

But why-o-why express it as if it were a formula, when it isn't?

I'm off for a cup of coffee to calm down.  Now, where's my calculator and formula booklet?

Shearer vs Savage (3-act-maths)

As part of the Sport Relief charity fundraising, Alan Shearer and Robbie Savage (now football pundits, previously players) are racing each other to sit on half of the seats at Wembley Stadium (the home of football in England).

Seems like a nice 3-act-maths problem to me.

The website for the programme is here.

Act 1
Show video of Robbie Savage sitting on chairs.  What is going on?
What question could we answer?  (how long it will take them to do it seems like an obvious one)
Give an estimate that you know is too high/low.

Act 2
What information do we need?
How long it takes to sit on each seat.  This can be timed from the video clip.
How long it takes to move between rows, blocks, etc.
Whether they will slow down as they get tired, or speed up as they develop a better technique.
How many seat there are in Wembley Stadium.  Wikipedia and the BBC claim 90,000 and appear to be using that as an exact figure.

Act 3
Well, at the moment (10th March 2014) there isn't an Act 3.  I want to use this in class tomorrow so we can then see later in the week how close we were.  Soon there will be an Act 3 video we can use!

Tetra-Tarsia

I had always assumed that the hexagonal tarsia were the coolest (start with triangles – make a hexagon – you can’t complain about that!).  A couple of weeks ago I discovered that the triangular ones are maybe even cooler.  Having finished the big triangle (and taped the pieces together rather than sticking them onto a piece of paper) pupils can then fold it up to make a tetrahedron.  First of all, few seem to realise that this is feasible (“so a triangle is really a net of a pyramid?”) but earlier finishers can also create their own question/answer combinations to go on the blank parts of the triangle that will be stuck together.

The one shown above comes from MrBartonMaths on TES.

Next step – I wonder if I can make my own ones with questions/answers on every side of the triangles so that it will make a complete tetrahedron.  Will pupils be able to work it out?