Angelina Jolie has had both breasts removed because of the risk of developing breast cancer.
But did she understand the Maths?
She may be right. This could be the best way for her to avoid breast cancer. And it IS her decision.
But maths isn’t that clear cut. Referenced information about BRCA1 and BRCA2: Cancer Risk and Genetic Testing can be found at The National Cancer Institute here.
in the general population will develop breast cancer sometime during their lives compared with about
60 percent of women (600 out of 1,000)
with gene mutation in BRCA1 or BRCA2. This is FIVE TIMES the risk over a lifetime.
BUT and this is a big but …..
It is important to note, however, according to The National Cancer Institute (USA), most
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research related to BRCA1 and BRCA2 has been done on large families with many individuals affected by cancer and the cancer risk associated with BRCA1 and BRCA2 mutations have been calculated from studies of these families. Because family members
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share a proportion of their genes and, often, their environment, it is possible that the large number of cancer cases seen in these families may be due in part to other genetic or environmental factors.
Factors that could affect these risk factors include food, lifestyle, location, inherited temperament and even the air they breathe.
Statistics are a useful tool. But statistics are based on random selection. This is IMPORTANT. Once you bias the data, your results are corrupted.
Removing cancerous breast tissue makes sense. Removing perfectly healthy breast tissue based on the maths … well … you’d want to think about it.
To put this another way the BRCA genes may be correlated with breast cancer, but this event is not independent of all other events in one family. There may be many, yet to be discovered, links . This is a common error in statistics made not only by journalists, but by experts too. (See below)
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Conviction by Maths Error
On 9 November 1998 at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two baby boys.
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Clark’s first son died suddenly within a few weeks of his birth in 1996. In 1998, when her second son died in similar circumstances she was arrested and tried for the murder of both sons.
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The prosecution used paedeatrician Prof Roy Meadows as a expert witness. He had discovered Munchausen Syndrome by Proxy (MSbP). Sally Clark was found guilty and spent 3 years in jail.
Prof Roy Meadows testified that the chance of two children from an affluent family suffering sudden infant death syndrome was 1 in 73 million. He arrived at this number by squaring 1 in 8500 for likelihood of a cot death in similar circumstances.
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He was wrong and was later struck off the medical registrar. He assumed that these were independent events. They were not. Maybe the heater was at fault. Or the cot. Or the house paint. Or, as suggested in The Observer article, faulty genes in the family.
Sally Clark died several years later of alcoholic poisoning. More information.
When Apple first released the iPod Shuffle it included a Random Play option from the owner’s playlist. People started complaining that ‘random ‘ option played the same track in a row or too often. Why?
Because random means any track is selected then that track goes back on the list and may or may not be selected again. To correct the ‘RANDOM’ problem Apple had to add an algorithm that stopped to many repeats.
Requirements: A coin for each student & smart board or data projector.
First ask your students to toss a coin 10 times each.
Ask each student how many heads in a row they threw.
Now ask students ‘Do you think it is possible to throw 10 heads in a row?
It can be done. Here is how you do it.
Derren Brown is a UK mentalist, magician, hypnotist and maths guru. He’s awesome. He shows audiences how a lack of understanding maths, especially probability, leads to misinterpreting the facts.
The Hunger Games is about MATHS. Here are some interesting Hunger Game statistics.
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THE PLOT:
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In Suzanne Collin’s book, The Hunger Games, 12 districts in the land of Panem are suppressed and controlled by a vicious elite, who dress like neon-coloured French courtesans.
Each year the cruel rulers select one teen of each sex between the ages of 12 and 18 from each district to become tributes, who must fight to the death in a televised, sponsor-supported media event called The Hunger Games, set in a staged wilderness.
Only one tribute can survive. Katniss Everdeen and Peeta Mellark from the poor coal-mining District 12 are the local tributes for that year and must play at being star-crossed lovers to gain sponsor support and survive.
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THE MATHS:
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Tributes are selected in a process called The Reaping. The names of the, approximately, 2,000 young people in each district are placed in separate barrels for males and females and the names are drawn out of these barrels BUT…
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12 year olds …….. 1 slip
13 year olds …….. 2 slips
14 year olds …….. 3 slips
15 year olds …….. 4 slips
16 year olds …….. 5 slips
17 year olds …….. 6 slips
18 year olds …….. 7 slips
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BUT you can gain extra ‘food’ if you accept for more name slips.
Gale Hawthorne (pictured above), Katnis’ friend from District 12, has 42 slips in the barrel. What are his chances?
We will assume that there are 1,000 teens of each sex in each district and an equal distribution – rounded off – for each age group to 1000/7 = 143
Or search topics on Youtube eg. Introduction to Conics Khan
Why Does Mathspig like The Kahn Academy? Because it’s:
1. Free.
2. Quick
3. Clear
4. Low-key
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Salman gives digital chalk-and-talk tutes like a teacher. He hand draws the equations and graphs. He uses a calculator from time to time, but he tends not to use whizz bang spreadsheet graphs or perfectly presented textbook equations. It’s a bit wobbly and it’s all coming from Salman’s head.
And students like this approach. It makes maths look do-able.
The tutes on Maths Online are produced by Aussie Maths teachers and they are very good. Mathspig, of course, imagined the quadratic function tutes might look something like this:
Newspaper and magazine editors urge their readers to ‘click-on our website poll’ and then they publish the results in the next issue. The newspaper may learn about their readership. This is useful information for marketing but otherwise useless. It’s like asking hat wearers if they wear hats. Let me guess the answer? D’uh!
Included here are some results of two self-selecting surveys, which not only reveal the standard useless statistics but also some highly questionable numerical outcomes. In the Esquire Magazine Survey of Drinking (Sept 2010) 82% of their readers, who were willing to answer a survey about their drinking habits (Whereby, for some reason. 1 beer = 2 drinks), have a University Degree or higher (Or, maybe, 50% of them lie!!!!) and in the Health and Fitness (Oct 2010) magazine survey - Guess what? – magically the numbers for all options add up to 100%. Neat! Didn’t anyone fit more than one category? (Assuming all readers of Health and Fitness mag who are bothered enough to answer a survey on fitness do some exercise.)
A survey is taken but the number of people surveyed is so small as to be irrelevant; not much better than simply asking your mum for her opinion and publishing the results.
Included here is a full-page Women’s Weekly (Oct 2010) ad for an Elizabeth Arden Anti-wrinkle Cream. Look at these wonderful statics. 92%… 85% …Wow! Look at the language. Gives eyes a ‘radiant and luminous look’ Sounds like the DEVIL!!!! Read the small print.
The survey was based on 30 participants and ‘results may vary’.
When the Numbers involved are so SMALL the % Stated is Meaningless.
Newspapers often state that a cancer rate has doubled or increased (See pic) by 28%. Those % changes can be meaningless. For instance, double nothing is still nothing. You need the actual numbers.
Here is a statistic taken from Men’s Health magazine (March 2010). According to the government funded Australian Institute of Health and Welfare the actual number of Australian males who presented with melanoma in 2005 was 6,044
or 0.549 in 1,000
or 1 in 2,000.
If these numbers increase by 28% the number of Australian men presenting with melanoma will be:
0.703 in 1,000
or ~ 2 in 3,000.
These numbers are not so alarming. Then again would you take any notice of statistics of a magazine that suggests a ‘sonic boom’ from a golf club is causing deafness!!!!!
Lotto draws are, as with coin flipping, Independent orUNRELATED EVENTS. Newspapers often publish the least drawn numbers prior to a major prize draw.
When on June 5 2008 the Powerball jackpot reached over $50 million, making it the biggest prize ever offered in any Australian lottery game at the time media commentators went crazy. ( See Crazy Lotto Lovers Go Bananas Again!)
The Today show on Ninesmsn website advised ‘The most-drawn Powerball numbers are 26, 22, 5, 39, 24 and 34. The least drawn numbers are 41, 32, 10, 43, 35 and 20.’ This information is worthless. These facts imply that the balls know whose turn it is and then can organise themselves so that those balls drop down the shoot. As if! The draw is random. Any number is possible.
The winning numbers, in drawn order, were: 5, 21, 11, 38 and 2, with the Powerball 33, with the final prize of $58,737,207.41
Poor old 41, 32, 10,43, 35 and 20 will have to wait for another turn!!!!!!!
The estimates of lifetime risk are about
Derren Brown is a UK mentalist, magician, hypnotist and maths guru. He’s awesome. He shows audiences how a lack of understanding maths, especially probability, leads to misinterpreting the facts.
