DAY 70 Covid-19 .. some CURIOUS Stats

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.

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

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!

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!!!!!!!

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

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:

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

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.

Winter Olympics: Bad Math of Figure Skating Scores

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

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

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

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

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!!!!

Mean, Median and Coffee: Busting an Urban Myth

 

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.

 

Lego Mean, Median, Mode

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.

Start with 40 bricks.

Sort into Stacks to create graph of

 No. Prongs Vs No. Bricks

This is a close up of the stacks above.

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

 

Dangerous Maths 1:Young drunk dead

Statistics for alcohol consumption are tricky. Binge drinking gets confused with heavy drinking. If you want to stay young go to the UK. They think anyone under 35 is a youth! Some stats separate Male and Female drinking habits. Some don’t. And legal drinking ages vary. Canada is one crazy place. It has different legal drinking ages in different parts of the country.

Legal Drinking Age:

The Maths

What we are working on here is reading maths data. No lectures. The numbers speak for themselves.

Graph source here

The Challenge

Find the following information from data below. Percentage of Year 12 students or 18 year olds who binge drink in each country below.

1. Australia

Graph Source here.

2. Canada

Graph Source here.

3. UK

Graph Source here

4. USA

Graph source here

Answers- Young drunk dead

Use these % to create a bar graph comparing countries. (Answer below)

Graph drawn using Create a Graph website

Alcohol related death stats over lap other stats including death involving cars, motorcycles, bicycles, skateboards, jet skis, quad bikes, drowning, diving, stairs, supermarket trolleys and even high heels.

photo source Daily Mail

Alcohol Related Youth Death Statistics

UK¹: 314

Australia2: 260

Canada³: 3,500

USA⁴: 4,358

1. 15-34 years for 2011. Source

2. 15-24 years average 1990-2002 Source

3. Under 18 years of age. 1996 It is believed that as many as 83 percent of teenagers in Canada consume alcohol. Back in 1996, underage drinking was responsible for 3,500 deaths and 2,000,000 injuries. A 2002 survey found that 20 percent of eight graders had consumed alcohol within the previous month. Source

4. 4,358 people under age 21 die each year from alcohol-related car crashes, homicides, suicides, alcohol poisoning, and other injuries such as falls, burns, and drowning. Source

These countries have different populations (See post below). USA population is 15 times Australia’s. 260 x 15 = 3,900. So the Aussie and US stats are in the same ball park even though the stats have been collected for different age ranges. But look at Canada. The USA population is about 9 times Canada’s. 4,358 ÷ 9 = 484 deaths. This  death statistic for Canada is 10 times larger than the USA statistic per head of population. Meanwhile, the population of Canada is 1 1/2 or 1.5 times Australia’s. 260 x 1.5 = 390. Once again, the Canadian statistic is out by a factor of 10. What’s going on here?

The Bar Where You’re Too Afraid to Get Smashed

Mathspig is a party pig. But why does anyone drink themselves senseless? Many reasons, but one is they’re bored. Now here is a bar in Mathspig’s home town, Melbourne, where you better stay sober. Break out of prison in Trapt Bar. You’re in prison, you’re innocent, and no one believes you. You plot an escape with the other prisoners–because unless you break free soon, you’ll all face an unspeakable death (this prison is off the charts). At Trapt Bar and Escape Rooms, you and your teammates have 45 minutes to find clues, solve puzzles and escape before…well…let’s spare you the gruesome details.

4. Why the best figure skater doesn’t always win

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.

Joannie Rochette

Brendan Kerry Australia…..

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

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

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

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!!!!

3. Stuff Ups 1

You go to the doctor with lower back pain.

The doc recommends an MRI scan. A problem is identified and an operation, perhaps, recommended. But here is the problem. The back problem identified in the scan may not be the cause of the pain.

In maths this is called FALSE ATTRIBUTION.

You get all the pain – financial and physical – but no gain.

You will find a very interesting discussion of this problem The Health Report, Radio National, ABC.

Dentists suffer a higher incidence of lower back pain … Maybe from prancing around in towels in front of mirrors. Wait. That was only a small sample of 10 paid dentists.

No conclusion can be drawn.