Archive for the ‘statistics’ Category

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Stranger Things Math 2: Now You are the Galton Ball

July 22, 2022

Mathspig has become obsessed with the Galton Board since watching ELEVEN dropping discs into the peg board on STRANGER THINGS 4.

Now thanks to David Butler, University of Adelaide, you can turn your middle school class into Galton Balls. You can find 100 randomly generated instruction sheets for each human Galton Ball at David’s website. (Link above)

Ideally, you would have 3,000 students to do this activity. But the class exercise ends with something approximating a Normal Distribution or Bell Curve constructed from video tap casettes. And the NOrMal Distribution is spooky.

More on the Galton Board Math here.

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Stranger Things Math: Eleven and the Galton Board

July 3, 2022

NOTE: Michael (above), who seems appropriately scary for this post, uses a commercial Galton Board.  It has one flaw. Many balls feed into the grid at once and this will change the pathways taken because the balls bump into one another. The best results come from dropping in the balls one at a time. If you had the patience to drop in 3,000 balls one at a time.

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NATHAN CHEN wins Gold but Figure Skating Scores can be BAD MATH

February 10, 2022

Nathan Chen, 22, USA, wins GOLD in the Men’s Figure skating with 5 brilliant, soaring quadruple jumps executed to perfection to Elton John’s “Goodbye Yellow Brick Road” and “Rocket Man.”

Nathan Chen’s Winning Performance on You tube HERE.

According to the fab NBC video, Mathletes,  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Tessa Virtue and Scott Moir(Above) GOLD Medal performance at Pyeongchang 2018 here.

Kailani Craine, Australia

figure skating score 9 judges nbclearn

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

figure skating score A

Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

7.00 + 7.00 + 7.00 + 6.75 + 7.00

……………………………………..

=  34.75/ 5 = 6.95

figure skating score B

Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

7.00 + 7.25 + 7.00 + 7.00 + 7.00

……………………………………..

=  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

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DAY 70 Covid-19 .. some CURIOUS Stats

April 4, 2020

Excellent Covid-19 stats update here.

If no preventative measures were taken by governments around the world then we could have been looking at a Plague Worse Case Scenario here.

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Eat Red Meat and Die ….. NOT NOW! ….. Maybe, sometime.

June 19, 2019

Here we go again.

“Eating even the moderate amounts of red and processed meat sanctioned by government guidelines increases the likelihood of developing bowel cancer” according to the above article in The Guardian, UK.

The sample size was 500,000. That’s good. It is a self-selecting sample. That’s not good. They could all be health fanatics. But here is the kicker:

“The researchers found those who ate the most and least red and processed meat tended to exaggerate their consumption or lack thereof.”

That’s a shock. People lie or exaggerate. Even the researchers then suggest – despite the screaming headline – that you don’t change your diet.

Although, looking at the plate above … I would!

Real Men Eat Red Meat and Die … Sometime!

Eat Meat and die??????

According to this headline in THE AUSTRALIAN 25th, March 2009   meat eaters are at risk of dying of cancer. The study published in  Archives of Internal Medicine involved half a million people over 10 years. So far so good. That is a good sample size. The sample consisted of people aged 50 to 71 years at baseline or, obviously, after 10 years 60 to 81years!!!!  So some deaths would be expected. Nevertheless, the article states: 

“Men whose red meat intake put them in the top 20 percent consumption band were 22 percent more likely to die of cancer in the 10 years of the study, compared to men whose intake was in the lowest 20 percent. For women, there was a 20 percent increase in risk.”

Here is the problem. Firstly and I quote from the original study: “Meat intake was estimated from a food frequency questionnaire administered at baseline.’ So they asked people once what their eating habits were then assumed they continued for the next 10 YEARS??? How likely are your eating habits to change in 10 years???

Secondly, and this was mentioned in the article without explaining the maths, big meat eaters tend also to be big drinkers, smokers, obese and the rest. This study has tried to separate out meat eating from other unhealthy lifestyle choices using the Cox Regression. Mathematical wizardry has produced these numbers but they don’t mean much. 

If the study used a control group of drinking, smoking, obese vegans then compared mortality rates over 10 years that would be interesting. But where do you find half a million of them???????? 

Finally,  the study  concluded ‘Red and processed meat intakes were associated with modest increases in total mortality, cancer mortality, and cardiovascular disease mortality.’ Not the stuff of headlines at all!!!!!!!

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Trick 9: Coin Trick. How to throw 10 HEADS in a row!!!!

April 30, 2018

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.

Now play this video to the students:

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Sasha a little dog with a BIG, BIG ID Number!

March 28, 2018

This exercise works best if for homework the middle school students count the digits in their own cell phone, passport, bill code or some other number. They don’t have to show the passport or bill. They just have to count the digits.

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Winter Olympics: Bad Math of Figure Skating Scores

February 22, 2018

According to the fab NBC video, Mathletes,  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018

                                   Kailani Craine, Australia

figure skating score 9 judges nbclearn

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

figure skating score A

Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

7.00 + 7.00 + 7.00 + 6.75 + 7.00

……………………………………..

=  34.75/ 5 = 6.95

figure skating score B

Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

7.00 + 7.25 + 7.00 + 7.00 + 7.00

……………………………………..

=  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

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Mean, Median and Coffee: Busting an Urban Myth

April 21, 2017

 

A Fun Maths Exercise.

Students count steps.

No units of length used. 

You can find the free pdf worksheet  (included below) here.

Other fun middle school math(s) worksheets in the Hot Heels series at TpT include

Unit Rates, Angles, Ratios and Algebra.


There is a lot of maths and science behind coffee sloshing in a coffee mug. ‘The human stride has almost exactly the right frequency to drive the natural oscillations of coffee’ explains fluid physicists at the University of California at Santa Barbara. You will find their full explanation here.

 

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Lego Mean, Median, Mode

January 15, 2016

Students can calculate the Mean, Median and Mode using Lego. Here is the exciting part:

The lego stacks become the graph

START with 40 LEGO BRICKS

Draw a graph of No. of Blocks Vs No. of Prongs (per block) Make sure all blocks are the same height.

Mean median mode Lego 1

Start with 40 bricks.

Mean median mode Lego 2

Sort into Stacks to create graph of

 No. Prongs Vs No. Bricks

Mean median mode Lego 2a

This is a close up of the stacks above.

Mean median mode Lego 3

The no. of bricks in each stack is written on top of the stack.