GCSE results: edging towards perfection
It seems that historic GCSE attainment data is hard to access. Understandably so. The government, and its predecessors for the last 29 years, hardly have a good story to tell.
Neither the ONS, nor DfE nor data.gov.uk seems able to furnish me with historic attainment figures. Specifically, I’d like the percentage of pupils attaining five or more A*–C grades by year. And I’d like to know the grade distribution by subject (and overall) by year.
I’ve managed to cobble together a dataset containing 2001/2 data and 2006/7 data showing the proportion of A*–C grades by primary subject by geography and gender. It seems that subsequent years’ data isn’t available. For the sake of brevity, let’s wrongly refer to an A*–C grade as a pass.
Over that five-year period, the pass rate in core subjects has gone up by 8.9 percentage points, from 31.6% to 40.5%. Assuming linearity, everyone should be passing these subjects by 2039.
Over the same period, Maths passes have risen by 4.7 percentage points, from 49.2% to 53.9%. And English by 4.2 points, from 56.8 to 61.0%.
So as a nation, it’s clear that we’re becoming more intelligent. Or are we?
Of course we’re not. The whole thing is a farce. The overall pass rate (in the ridiculous “turn up and you pass” sense of the word) has risen for the 23rd consecutive year, now sitting at a heady 98.7%. The qualification has become meaningless. A grades were the first to become worthless, A* grades being introduced in 1994, soon becoming the new currency of choice. And now in certain circles, anything less than ten results containing the letter A is seen as failure. How on earth employers or colleges evaluate the relative merit of candidates I have no idea.
As I’ve said before, there needs to be some normalisation. We are not getting more intelligent as a nation. The percentage of A* grades awarded each year should not change. Ever. There should be a forced curve for each subject. It would give predictability to those organisations interested in those pupils. But perhaps more importantly, it would rid the world of trite, vacuous news stories every August, accompanied by attractive leaping girls.
This won’t happen, of course. Instead, the youth of tomorrow will edge towards perfection, everyone becoming equal and indistinguishable.
Shopping odds
I played the shopping game with my daughter, panda and monkey last night. There are 32 cards, each portraying an item of shopping, all placed face down. Each of us has a flat, cardboard shopping trolley that can hold eight items, and a shopping list containing eight items.
The objective is to fill your shopping trolley with the items on your list by uncovering the cards, one at a time. Our simplified rules dictate that if you uncover one of your opponent’s items, they can put it in their trolley and take the next turn.
My daughter had six items in her trolley before anything was uncovered belonging to me. Panda had seven. And monkey had five. So 18 cards had been uncovered without a single one belonging to me.
The odds of this happening to me were 1,436,568 to 1. The odds of it happening to one of us were 359,142 to 1.
My first 100-comment post
Today marked a milestone for Tangential Ramblings. One of my posts notched up an incredible 100 comments.
To put that into perspective, the entire blog has recorded 2,349 comments across its 1,703 posts, an average of 1.38 comments per post. If I blogged to generate comment, I would have given up the best part of seven years ago.
Putting aside the 100-comment post for a moment, the next most comment-heavy post has seen 17 comments, and only six posts have hit double-figures.
The post that has stood out as an outlier is titled iTunes cannot read the contents of your iPhone [solved]. Its title is an iPhone error message that I encountered some 12 months ago, one that I researched and eventually solved. There wasn’t a single solution out there that I could use, so I wrote one.
And in so doing, I’ve helped 100 people who’ve suffered the same issue who were happy to comment. And, I expect, ten times that number who haven’t commented.
That’s reward in itself.
For those that are interested, below are the top seven posts by number of comments:
- iTunes cannot read the contents of your iPhone [solved]: 100 comments
- Grouping of phone numbers: 17 comments
- Pi to 110,100 binary places: 11 comments
- How are you? Not bad: 10 comments
- SUMPRODUCTIF: 10 comments
- Invention: Sellotape with a coloured tear: 10 comments
- The happiest day of my life: 10 comments.
Diabetes: lies, damned lies and statistics
On Sunday, BBC News ran a story about diabetes. It drew facts from a study in the Lancet and focused on the fact that the number of people suffering from diabetes worldwide had more than doubled since 1980. But the article’s title read as follows:
Diabetes rate ‘doubles’ – Imperial College and Harvard research suggests
I took huge issue with the word rate. Here’s why.
The world’s population in 1980 was 4,435m. The Lancet estimated that 153m of those people suffered from diabetes, an incident rate of 3.45%.
In 2011, the world’s population has increased to 6,930m, the Lancet estimating that 347m of these suffered from diabetes, an incident rate of 5.01%.
The rate of diabetes has indeed increased. It has increased by 45%. It certainly has not doubled.
It frustrates me that such a qualified and reputable news source as the BBC can misleadingly report because a failure to understand such a basic mathematical concept.
Some impressive Premier League/Premiership stats
During the 15 years for which the Premiership/Premier League has consisted of 20 teams (excluding the as yet incomplete 2010/11 season):
- Man. Utd. has the best average finishing position: 1.6th
- Watford has the worst: 20th (in both of its seasons)
- Man. Utd. has scored the most goals: 1,150
- Of the seven teams to have competed in all 15 seasons (Aston Villa, Liverpool, Arsenal, Man. Utd., Spurs, Chelsea, Everton), Everton has scored the fewest: 734
- Of these seven teams, Everton has let in the most goals: 725. Man. Utd. the fewest: 493
- Man Utd. has won 13% more games than any other club (372), Arsenal being second with 329
- Spurs has the most losses (211) followed by Everton (205)
- Man Utd. has scored 1,230 points (2.16 per game), 8.6% more than its nearest rival (Arsenal: 1,133; 1.99 per game)
Impressive.
Premier League: points needed to avoid relegation/win the league
Since the 1995/6 season, when the Premiership was reduced to 20 teams, the best-placed relegated team (that in 18th-place) in the top flight has had:
- 30 points: once (2009/10)
- 33 points: three times (1999/2000, 2003/04, 2004/05)
- 34 points: three times (2000/01, 2005/06, 2008/09)
- 36 points: three times (1998/99, 2001/02, 2007/08)
- 38 points: twice (1995/96, 2006/07)
- 40 points: twice (1996/97, 1997/98)
- 42 points: once (2002/03).
This is the number of points that you’d need to exceed to stay in the league. This season, 39 looks certain to get you relegated.
At the top, the second-placed team (the number to exceed to win the league) has had:
- 68 points: once (1996/97)
- 70 points: once (2000/01)
- 73 points: once (1999/2000)
- 77 points: once (1997/98)
- 78 points: three times1995/96, 1998/99, 2002/03)
- 79 points: once (2003/04)
- 80 points: once (2001/02)
- 83 points: three times (2004/05, 2005/06, 2006/07)
- 85 points: twice (2007/08, 2009/10)
- 86 points: once (2008/09).
This season it looks like being a mere 73.
So this season has seen more competitiveness from the lower teams, leaving less spoils for the top teams.
Dalglish vs. Hodgson
I’m impressed with how Kenny Dalglish has managed Liverpool since he took over on 8 January. So much so that I decided to create a spreadsheet to compare his performance with that of Roy Hodgson. Below is a summary of the results.
In the Premier League:
- Dalglish: Managed 16. Won 10 (62.5%), Drew 3 (18.8%), Lost 3 (18.8%)
- Hodgson: Managed 20. Won 7, (35.0%), Drew 4 (20.0%), Lost 9 (45.0%)
Dalglish has averaged 2.06 points per Premier League game, to Hodgson’s 1.25. Incredibly, Dalglish would have averaged 2.06 points per game had all of his games finished at half time too. Hodgson would have averaged a meagre 1.15. Unfortunately, for Liverpool, the average points per game across the two managers was 1.61, not sufficient to trouble the top of the table.
In the Premier League, Dalglish has won four (50.0%) of his eight away games, drawing a further one (12.5%). Hodgson won one (10.0%) of his ten away games, drawing a further two (20.0%). In front of the Kop, Dalglish has won six (75.0%) and drawn two (25.0%). Not a loss in sight. Hodgson won six (60.0%), drew two (20.0%) and suffered two (20.0%) losses.
In Hodgson’s nine losses, his team lost by an average of 1.67 goals. Dalglish’s team lost by an average of 1.33 goals in their three losses. (This number is, by its very nature, always greater than or equal to one, btw.) Dalglish’s winning margin is a staggering 2.5 goals per game compared to Hodgson’s 1.71. Across all Premier League games, Dalglish racked up an average of 2.19 goals per game, letting in an average of 0.88; Hodgson’s team averaged 1.20, letting in 1.35.
At half time, Hodgson’s average was 0.5 goals for and 0.5 goals against. Dalglish averaged 1 goal for and a mere 0.19 goals against.
In Europe (including qualifying), Hodgson performed better, although he would have managed the easier games at the start of the season:
- Dalglish: Managed 4. Won 1 (25.0%), Drew 2 (50.0%), Lost 1 (25.0%)
- Hodgson: Managed 10. Won 6 (60.0%), Drew 4 (40.0%)
Across all competitions, Dalglish has won 11 (52.4%) of his 21 matches, Hodgson winning 13 (38.2%) of his 34, again inflated by early European competition.
Dalglish’s record in the FA Cup is less rosy. One game played, one game lost. 1–0 away at Old Trafford. It was on his second day in charge though.
Fuel prices vs. car prices
I filled up the hire car today. It had a quarter of a tank remaining, but my obligation as a hirer is to fill it up if it dips below that level. So I did. It cost £67 for standard unleaded, at 137.9p per litre. (BTW, that’s £6.27 per gallon in old money, as my dad, and oodles of other dads, still say to this day.) That would make it around £89 for a full tank by my reckoning. Ouch.
I got to thinking about what fuel efficiency was worth when purchasing a new car.
Having done the analysis it seems that, to me, marginal fuel efficiency has a surprisingly small impact on the cost of car ownership. At 12,000 miles per year, a car running at 40 miles per gallon will guzzle 300 gallons per year at a cost of £1,880.72. At 41 mpg, the cost will be £1,834.85, an annual drop of a mere £45.87, less than a pound a week. And obviously, as the mpg increases, the marginal price differential of a single extra mpg reduces. So the difference between the fuel costs for a 50 vs. 51 mpg car falls to £29.50.
So assuming depreciation over five years and other things being equal, a new car offering 45 mpg can justify being priced £1,044 higher than one offering 40 mpg.
Now switch your attention to the gas guzzlers. A car running at 10 mpg will cost £2,507 more per year to run than one running at 15 mpg, so the more fuel-efficient 15 mpg-er can justify a price tag £12,538 higher than the 10 mpg-er. As an aside, for such cars to average 12,000 miles per year, the school to which the car is driven twice daily would need to be 15.8 miles from the home. 
(Environmental arguments were left to one side in the writing of this post.)
Crowdsourcing lunacy
Back in October 2010, people were lauding that the month was the first in hundreds of years that featured five Fridays, five Saturdays and five Sundays. And this month, people are similarly bowled over about the rarity with which we witness a month that contains five Saturdays, Sundays and Mondays.
Immediately upon hearing the first example, I knew it was bunkum. But this time, I decided to document the idiocy.
Every single year features no fewer than seven months containing 31 days. This is a prerequisite for three separate days to appear five times. And in those months, the days that fall on the first, second and third of the month will feature five times. It’s as simple as that.
Now over the course of time, the probability of each day of the week hitting the first day of one of those months tends to 1/7, or 14.28%. So the first of January in a randomly chosen year is (roughly) equally likely to fall on a Monday, a Tuesday, Wednesday, Thursday, Friday, Saturday or Sunday.
And given that there are seven candidate months each year, you should expect to see an average of one month a year containing five Fridays, Saturdays and Sundays. Or any other combination of three consecutive days for that matter.
The likelihood of getting five Saturdays in February on the other hand is much smaller. It happened three times in the 20th century (1920, 1948 and 1976) and will next happen in 2032. *That* would be something worth writing about, were it not for the lunacy that is the Gregorian calendar.
Prime time
There was a bit of a Twitter storm earlier today. Someone decided it would be fun to extol the virtues of 2011 by proclaiming that the number 2011 was the sum of eleven consecutive primes: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 and 211. Oh, and there were further palpitations at the fact that 2011 is itself prime.
I was out on the street at the time. But the incredulity that this phenomenon was drawing from the Twitter crowd seemed in my head to be unwarranted. So when I got home, I did some analysis. Some lovely analysis.
First things first, the smallest number for which the above is true is 160—the sum of the first eleven primes. Not a prime itself though. The smallest prime that is the sum of eleven consecutive primes is 233.
Analysing all years from AD 1 to AD 3000 (to give us some room for giddiness in the years to come), 40.4% of them are the sum of two or more consecutive primes. (I ruled out those that are merely the sum of a single [consecutive] prime, as their names shouldn’t really be on the door.) That’s right: 1,213 are the sum of two or more consecutive primes.
Fifty-seven of them are sums of 30 or more consecutive primes, our stellar performer being 2914, the sum of 39 consecutive primes. If the number itself has to be prime (as 2011 is), then 2909 is the sum of 37 consecutive primes (all primes between five and 167 inclusive).
To more immediate times. The miraculous feat of 2011 will be surpassed in 2016 (18 consecutive primes), while Twitter will likely come crashing to its knees in 2027 as people retweet the fact that as well as the year itself being prime, it is the sum of a whopping 25 consecutive primes.
As for recent past, 1999 (prime) was the sum of nine. But wait for this: 1986 was the sum of 32, 1987 (prime) the sum of 19, and 1988 the sum of 33. Can you imagine if Twitter had been around then?
Arseholes.