statistics
https://plus.maths.org/content/taxonomy/term/705
enMaths in a minute: The central limit theorem
https://plus.maths.org/content/maths-three-minutes-central-limit-theorem
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<p>Opinion polls, election forecasts, testing new medical drugs — none of these would be possible without the central limit theorem.</p>
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<p>The central idea in statistics is that you can say something
about a whole population by looking at a smaller sample. Without this
idea there wouldn't be opinion polls or election forecasts, there would be no way of testing new medical drugs, or
the safety of bridges, etc, etc. It's the <em>central limit theorem</em>
that is to a large extent responsible for the fact that we can do all
these things and get a grip on the uncertainties involved.</p><p><a href="https://plus.maths.org/content/maths-three-minutes-central-limit-theorem" target="_blank">read more</a></p>https://plus.maths.org/content/maths-three-minutes-central-limit-theorem#commentscentral limit theoremstatisticsTue, 19 Apr 2016 14:46:41 +0000mf3446548 at https://plus.maths.org/contentStop taking the p
https://plus.maths.org/content/stop-taking-p
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/7_apr_2016_-_1356/data_icon.jpg?1460037375" /> </div>
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<p>Why a time-honoured statistical tool is becoming problematic.</p>
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<p>"Lies, damned lies, and statistics" — considering the deluge of data
the modern world is showering us with, this <a href="https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics">famous quote by Benjamin Disraeli</a> seems all
the more relevant. Science, as well as policy making, rely on
statistical analyses of this data wealth, which makes them vulnerable to statistical
mischief.<p><a href="https://plus.maths.org/content/stop-taking-p" target="_blank">read more</a></p>https://plus.maths.org/content/stop-taking-p#commentshypothesis testingnull hypothesisp valuesignificance teststatisticsTue, 12 Apr 2016 10:37:42 +0000mf3446544 at https://plus.maths.org/contentSexual statistics: The podcast
https://plus.maths.org/content/sexual-statistics-podcast
<div class="rightimage" style="width: 150px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/articles/2015/sex/cover.png" width="150" height="239" alt="Book cover"/></div>
<p>Every day we are bombarded with statistics about sex. How many times we think of it a day, how many times we do it, and with how many people. But how do we know which of those numbers can be believed? </p><p><a href='http://plus.maths.org/content/sites/plus.maths.org/files/articles/2015/sex/david_s_audio.mp3'>Listen to our interview with David Spiegelhalter</a></p><p><a href="https://plus.maths.org/content/sexual-statistics-podcast" target="_blank">read more</a></p>https://plus.maths.org/content/sexual-statistics-podcast#commentssocial statisticsstatisticsThu, 02 Apr 2015 12:24:26 +0000mf3446339 at https://plus.maths.org/contentSexual statistics
https://plus.maths.org/content/sexual-statistics
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The Plus Team </div>
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<p>David Spiegelhalter's new book <em>Sex by numbers</em> takes a statistical peek into the nation's bedrooms. In this interview he tells us some of his favourite stories from the book. Read the article or watch the video!</p>
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<div style="float:right"><iframe width="400" height="225" src="https://www.youtube.com/embed/ksx9UETAJ4g" frameborder="0" allowfullscreen></iframe>
<p style="width: 400px; font-size: small; color: purple;">Watch the full interview with Spiegelhalter in this video or listen to it as a <a href="https://plus.maths.org/content/sexual-statistics-podcast">podcast</a>.</p><p><a href="https://plus.maths.org/content/sexual-statistics" target="_blank">read more</a></p>https://plus.maths.org/content/sexual-statistics#commentssocial statisticsstatisticsvideoThu, 02 Apr 2015 10:36:45 +0000mf3446338 at https://plus.maths.org/contentMaths in a minute: What's average?
https://plus.maths.org/content/maths-minute-all-about-averages
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/10_feb_2015_-_1136/icon.jpg?1423568185" /> </div>
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<p>Why the humble average can be grossly misleading.</p>
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<p>Most people have more than the average number of ears. This might seem odd, but it's true. The vast majority of people have two ears, but the few who have only one or none bring the average down to less than two. It's easy to illustrate this by imagining there are only five people in the world with one of them having only one ear. The average number of ears is </p><p><a href="https://plus.maths.org/content/maths-minute-all-about-averages" target="_blank">read more</a></p>https://plus.maths.org/content/maths-minute-all-about-averages#commentsaveragemedianmodestatisticsTue, 10 Feb 2015 11:34:20 +0000mf3446310 at https://plus.maths.org/contentGood-looking gibberish
https://plus.maths.org/content/good-looking-gibberish
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<p>How to approximate the English language using maths.</p>
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<p>How would you approximate the English language? In the 1940s the mathematician <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Shannon.html">Claude Shannon</a> asked himself just this question. Given a machine that can produce strings of letters, how would you set it up so that the strings it produces resemble a real English sentence as closely as possible?</p>
<div class="rightimage" style="width: 262px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/news/2015/shannon/shannon.png" width="262" height="324" alt="Claude Shannon"/><p>Claude Shannon.</p><p><a href="https://plus.maths.org/content/good-looking-gibberish" target="_blank">read more</a></p>https://plus.maths.org/content/good-looking-gibberish#commentsInformation theorymathematics and languagestatisticsMon, 09 Feb 2015 10:36:57 +0000mf3446307 at https://plus.maths.org/contentThe leaning tower of PISA?
https://plus.maths.org/content/leaning-tower-pisa-0
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/4_dec_2013_-_1655/school_icon.jpg?1386176139" /> </div>
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<p>This year's PISA results have caused predictable headlines, but do the statistics add up?</p>
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<p> According to the latest <a href="http://www.oecd.org/pisa/keyfindings/pisa-2012-results.htm">PISA</a> study
Britain's teenagers have dropped out of the top 20 in reading,
maths and science. That's in a ranking of 65
economies from around the world. Media reactions were
predictable (worse than <em>Estonia?!</em>) and so were <a href="http://www.theguardian.com/politics/2013/dec/01/michael-gove-labour-international-league-table">Michael Gove's</a>
(it's the last government's fault), but some were a little more
critical.<p><a href="https://plus.maths.org/content/leaning-tower-pisa-0" target="_blank">read more</a></p>https://plus.maths.org/content/leaning-tower-pisa-0#commentsmathematics educationstatisticsThu, 05 Dec 2013 16:56:34 +0000mf3445990 at https://plus.maths.org/contentUnderstanding uncertainty: ESP and Bayes
https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes
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Kevin McConway </div>
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<p>In the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?</p>
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<div align="center" style="margin:auto;width:400px; font-size:15; border: #9a7a9f 2px solid; padding:5px;">This article has been adapted from material on the <a href="http://understandinguncertainty.org/node/1286">Understanding Uncertainty website</a>.</div> <p><a href="https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-esp-and-bayes#commentsbayes theoremconditional probabilityp-valueprobabilitypsychologysignificance teststatisticsunderstanding uncertaintyMon, 15 Oct 2012 15:48:39 +0000mf3445782 at https://plus.maths.org/contentUnderstanding uncertainty: ESP and the significance of significance
https://plus.maths.org/content/esp-and-significance-significance
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Kevin McConway </div>
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<p>In March 2011 a highly respected psychology journal published a paper claiming to provide evidence
for extra-sensory perception (ESP). The claim was based largely on the
results of a very common statistical procedure called significance testing. The experiments
provide an excellent way into looking at how significance testing
works and at what's problematic about it.</p> </div>
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<div align="center" style="margin:auto;width:400px; font-size:15; border: #9a7a9f 2px solid; padding:5px;">This article has been adapted from material on the <a href="http://understandinguncertainty.org/node/1286">Understanding Uncertainty website</a>.</div> <br />
<div class="rightimage" style="width: 313px"><img src="/sites/plus.maths.org/files/articles/2012/esp/psychic.jpg" alt="Psychic" width="313" height="238" />
<p>Is there such a thing as extra-sensory perception? Image: <a href="http://en.wikipedia.org/wiki/File:PsychicBoston.jpg">Boston</a>.</p><p><a href="https://plus.maths.org/content/esp-and-significance-significance" target="_blank">read more</a></p>https://plus.maths.org/content/esp-and-significance-significance#commentsp-valueprobabilitypsychologysignificance teststatisticsunderstanding uncertaintyMon, 15 Oct 2012 14:46:34 +0000mf3445781 at https://plus.maths.org/contentCounting deaths: war as a statistical problem
https://plus.maths.org/content/counting-dead-war-statistical-probelm
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<p>How many people died? It's one of the first questions asked in a war or violent conflict, but it's one of the hardest to answer. In the chaos of war many deaths go unrecorded and all sides have an interest in distorting the figures. The best we can do is come up with estimates, but the trouble is that different statistical methods for doing this can produce vastly different results . So how do we know how different methods compare?</p>
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How many people died? It's one of the first questions asked in a war
or violent conflict but it's one of the hardest to answer. In the chaos of war many deaths go unrecorded and all sides have an interest in
distorting the figures. </p><p><a href="https://plus.maths.org/content/counting-dead-war-statistical-probelm" target="_blank">read more</a></p>https://plus.maths.org/content/counting-dead-war-statistical-probelm#commentsconfidence intervalstatisticssurveyuncertaintyThu, 23 Feb 2012 09:35:09 +0000mf3445666 at https://plus.maths.org/contentUnderstanding uncertainty: Visualising probabilities
https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities
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Mike Pearson and Ian Short </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/19_oct_2011_-_1700/icon_risk.jpg?1319040008" /> </div>
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<p>Probabilities and statistics: they are everywhere, but they are hard to understand and can be counter-intuitive. So what's the best way of communicating them to an audience that doesn't have the time, desire, or background to get stuck into the numbers? This article explores modern visualisation techniques and finds that the right picture really can be worth a thousand words.</p>
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<p><em>Probabilities and statistics: they are everywhere, but they are hard to understand and can be counter-intuitive. So what's the best way of communicating them to an audience that doesn't have the time, desire, or background to get stuck into the numbers? Ian Short explores modern visualisation techniques and finds that the right picture really can be worth a thousand words. </em></p><p><a href="https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities" target="_blank">read more</a></p>https://plus.maths.org/content/understanding-uncertainty-visualising-probabilities#commentsCMSprobabilityriskstatisticsuncertaintyunderstanding uncertaintyvisualisationMon, 31 Oct 2011 09:09:35 +0000mf3445572 at https://plus.maths.org/contentAnyone for tennis (and tennis and tennis...)?
https://plus.maths.org/content/anyone-tennis
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Mark A. Thomas </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/19_may_2011_-_1501/icon.jpg?1305813678" /> </div>
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<p>As the Wimbledon 2011 Championships hove into view, memories will be reawakened of the match of epic proportions that took place last year between the American John Isner and the Frenchman Nicolas Mahut. So just how freaky was their titanic fifth set and what odds might a bookmaker offer for a repeat?</p>
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<div class="rightimage" style="width: 430px"><img src="/sites/plus.maths.org/files/articles/2011/tennis/isner_mahut.jpg" alt="John Isner" width="430" height="181" />
<p>Nicolas Mahut (left, image <a href="http://en.wikipedia.org/wiki/File:Nicolas_Mahut_at_the_2009_Wimbledon_Championships_01.jpg">Bruno Girin</a>) and John Isner (right, image <a href="http://en.wikipedia.org/wiki/File:John_Isner_at_the_2009_US_Open_01.jpg">Charlie Cowens</a>).</p><p><a href="https://plus.maths.org/content/anyone-tennis" target="_blank">read more</a></p>https://plus.maths.org/content/anyone-tennis#commentsbernoulli trialgeometric distributionmathematics in sportprobabilitystatisticsFri, 03 Jun 2011 09:10:47 +0000mf3445487 at https://plus.maths.org/contentMeasuring catastrophic risk
https://plus.maths.org/content/misinterpretation-risk-metrics
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Shane Latchman </div>
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<p>Insurance companies offer protection against rare but catastrophic events like hurricanes or earthquakes. But how do they work out the financial risks associated to these disasters? Shane Latchman investigates.</p>
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<h3>The notion of uncertainty</h3>
<p>In the early 19th century, the French mathematician <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Laplace.html">Pierre-Simon de Laplace</a> wrote of a concept he had been thinking about for some time. The concept became known as <em>Laplace's demon</em> and was a thought experiment which sought to clearly explain the existence of uncertainty. It is described in his <em>Essai Philosophique sur les Probabilités</em> (1814) as:
</p><p><a href="https://plus.maths.org/content/misinterpretation-risk-metrics" target="_blank">read more</a></p>https://plus.maths.org/content/misinterpretation-risk-metrics#commentsconfidence intervalearthquakesinsurancemathematical modellingprobabilityriskrisk analysisstatisticsThu, 23 Dec 2010 14:36:31 +0000mf3445360 at https://plus.maths.org/contentFlorence Nightingale: The compassionate statistician
https://plus.maths.org/content/florence-nightingale-compassionate-statistician
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Eileen Magnello </div>
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<p>Florence Nightingale died a hundred years ago, in August 1910. She survives in our imaginations as an inspired nurse, who cared passionately for injured and dying soldiers during the Crimean war, and then radically reformed professional nursing as a result of the horrors she witnessed. But the "lady with the lamp" was also a pioneering and passionate statistician. She understood the influential role of statistics and used them to support her convictions. So to commemorate her on the centenary of her death, we'll have a look at her life and work as a statistician.</p>
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<p><em>Florence Nightingale died a hundred years ago, in August 1910. She survives in our imaginations as an inspired nurse, who cared passionately for injured and dying soldiers during the Crimean war, and then radically reformed professional nursing as a result of the horrors she witnessed. But the "lady with the lamp" was also a pioneering and passionate statistician. She understood the influential role of statistics and used them to support her convictions. So to commemorate her on the centenary of her death, we'll have a look at her life and work as a statistician.</em></p><p><a href="https://plus.maths.org/content/florence-nightingale-compassionate-statistician" target="_blank">read more</a></p>https://plus.maths.org/content/florence-nightingale-compassionate-statistician#commentscoxcombmedical statisticsmedicine and healthNightingalestatisticsWed, 08 Dec 2010 12:04:13 +0000mf3445356 at https://plus.maths.org/contentHow to protect your privacy
https://plus.maths.org/content/how-protect-your-privacy
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<p>How would you feel if your private health record were revealed to insurance companies or prospective employers? These days our details are kept on all sorts of different databases and cleverly cross-referencing them can reveal intimate information about individuals. So what can be done to protect privacy? We talk to Cynthia Dwork from Microsoft Research, whose talk at the ICM showcased some mathematical tools to keep our details safe.</p><p><a href='http://plus.maths.org/content/sites/plus.maths.org/files/podcast/queries_0.mp3'>How to protect your privacy</a></p>https://plus.maths.org/content/how-protect-your-privacy#commentsrandomnessstatisticsTue, 24 Aug 2010 10:01:44 +0000mf3445292 at https://plus.maths.org/content