Student pages - obsolete

6950 /www/nrich/html/content/id/6950/ 5 2013-01-22T10:36:39 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">This page has permanently <a href="http://nrich.maths.org/secondary-upper">moved to here</a> following a major site redesign in 2012. Apologies for the inconvenience.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">This problem develops a very important skill of working with large sets of numbers and getting a 'feel' for their properties. This is an advanced mathematical artform and develops with experience and exposure. You can think of this problem as numerical detective work. If you enjoy this task you may find that you will be well suited to working as an industrial mathematician. In industrial and research applications large volumes of data are routinely used. Being able quickly to spot anomalous data can save huge amounts of time and effort. Unfortunately, in large real-world applications of statistics and mathematics errors and bugs in software are unavoidable and may only manifest themselves after months or even years of use. In addition, the computer software can run in length to millions of lines of code and it may take hours or even days to run the programme to generate the numbers in the first place. Clearly tracking down these bugs is a tricky task, and the data are often the first place to begin to try to narrow down the search. At A-level, checking answers is a crucial part of mathematical development and this problem will develop this skill. It also raises several interesting statistical points and the statistical ideas concerning the likelihood of the explanation of the errors being correct are important. Discussion should follow this problem about <ul> <li>What makes a 'good' explanation and what makes a 'bad' explanation?</li> <li>Can we ever be sure that our explanation is correct?</li> <li>At what point do we accept our explanation as correct?</li> <li>Suppose that we have found a scheme with an error.</li> <li>Can we calculate the chance that the 'error' has occurred by an unlikely event and is therefore an 'outlier'</li> </ul> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">For processes 1 to 4 you should be able to spot the odd one out simply by looking at the numbers carefully. For processes 5 and 6 you will need to experiment on a calculator. The processes are arranged in approximate order of difficulty. You might first like to generate lots of sets of the random numbers so that you can get a feel for the the patterns in the randomness. Start off by looking to see what sorts of things the numbers have in common and how they may logically be generated. Once you have a logical method of generation (which is only a guess, of course) you can check to see whether all but one of the numbers fits that method of generation. If you think that you have found an explanation, consider the likelihood of numbers generated by some other method accidentally fitting your pattern </mdoxml> 2 3 0 0 1 1 0 Student pages - obsolete This page has permanently moved