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Work in the media? Struggle with statistics? Stan's irreverent (and often irrelevant) review of the latest media reports, news and gossip may not help at all... Stan the Statistician

Stan # 95: Popular balls and optimal bottoms April 2009


The most popular winning numbers in the UK lottery are 38, 44, 43, 25, 47 and 23. So, all you have to do is choose these every week and you are sure to win. Or not. Maybe these numbers have ‘had their turn’ and now they should be given a rest. Maybe if people know that these are the most popular numbers, they will also choose them and the jackpot would have to be divided amongst more pople. The problem is that the balls have no memory. They don’t know that their colleagues have been selected more times than other numbers. They don’t have meetings to discuss these issues - whose turn it should be next. Perhaps it’s just as well that the numbers selected are purely random and which numbers have come up previously is completely irrelevant. If people understood probablity, they would be unlikely to treat gambling as a way of becoming rich. If betting was a way to Easy Street, bookmakers would go out of business. A flutter can be fun but more is the way to Skid Row.

Unix time reached 1,234,567,890 decimal seconds on February 13, 2009 at 23:31:30 GMT. I trust you celebrated appropriately. To remind you of the need to celebrate, the asteroid 2004 MN04 will make its close encounter on Friday, April 13, 2009.

Unix time, or POSIX time, is a system for describing points in time, defined as the number of seconds elapsed since midnight Universal Time (UTC) of January 1, 1970, not counting leap seconds. It is widely used not only on Unix-like operating systems but also in many other computing systems. It is neither a linear representation of time nor a true representation of UTC (though it is frequently mistaken for both) as the times it represents are UTC but it has no way of representing UTC leap seconds (e.g. 1998-12-31 23:59:60).

Modern Unix time is based strictly on UTC. UTC counts time using SI seconds and breaks up the span of time into days. UTC days are mostly 86400 s long, but due to "leap seconds" are occasionally 86401 s and could be 86399 s long (though the latter option has never been used as of January 2008). This is in order to keep the days synchronised with the rotation of the Earth (or Universal Time).

The Unix epoch is the time 00:00:00 UTC on January 1, 1970. There is a problem with this definition, in that UTC did not exist in its current form until 1972.

The Unix time number is zero at the Unix epoch, and increases by exactly 86400 per day since the epoch. Thus 2004-09-16T00:00:00Z, 12677 days after the epoch, is represented by the Unix time number 12677 × 86400 = 1095292800. This can be extended backwards from the epoch too, using negative numbers; thus 1957-10-04T00:00:00Z, 4472 days before the epoch, is represented by the Unix time number -4472 × 86 400 = -386380800.

Within each day, the Unix time number is as calculated in the preceding paragraph at midnight UTC (00:00:00Z), and increases by exactly 1 per second since midnight. Thus 2004-09-16T17:55:43.54Z, 64543.54 s since midnight on the day in the example above, is represented by the Unix time number 1095292800 + 64543.54 = 1095357343.54. On dates before the epoch the number still increases, thus becoming less negative, as time moves forward.

The above scheme means that on a normal UTC day, of duration 86400 s, the Unix time number changes in a continuous manner across midnight. Party-givers may like to hold discussions or lectures in the time leading up to the Big Moment.

David Holmes, a psychology professor at Manchester Metropolitan University, has devised a formula for the perfect posterior. First, he identified five key hindquarter attributes: shape (S) (scoring 1-4 where 4 is the highest), circularity or roundness (C) (again scoring 1-4 where 4 is the highest), bounciness or wobble (B) (scoring 1-5 this time where 5 is the highest), firmness (scoring 1-5 where 5 is the highest), skin texture (T) (scoring 1-5 where 5 is the highest) and hip to waiste ratio (V) (scoring 1-4 where 4 is the highest).

Next on the basis of self-assessments of 2,000 British woman, he came up with the formula (S+C) X (B+F) / (T-V) to produce a perfect score which might be regarded as the bottom line. Eighty is the perfect score. Yet a bottom can only be regarded as beautiful relative to the rest of a woman’s proportions. Statistics have demonstrated that more women conform to the pear or apple shape, or even the courgette shape than the highly-coveted hour glass (flaunted by only 8% of the population).

Of course, the appeal of shapes has changed over the years with Rubens, for example, popularising the ample rear. Today, the most popular bums can be typified by J-Lo, Kelly Holmes and of course, Kylie.

My concern over this formula is that it is based on self-assessment and how do these 2,000 women judge their behinds on the scales? They must surely be comparing them with other women and do they have a large enough sample? Have they really examined other women’s bottoms so closely? Does self-esteem play a part? I think it would be better to have the measurements carried out independently on a randomly selected sample rather than a self-selecting sample. I am sure we could find plenty of volunteers for the measuring but I’m not so sure we would obtain a balanced sample of either measurers or measurees. Would fatigue set in? It could be argued that you would have to be unbalanced to be a subject or a tester.

Check in again at my desk soon!

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