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.

 

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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.

4. Stuff Ups 2

All medical tests are subject to a % error.

This is a FALSE POSITIVE.

This may not be a problem if you are advised to, say, take more Vitamin D to correct the problem you don’t have. But if you are being advised to undergo major surgery, a second test is advisable.

As statistician Michael Blastland explained in Everyday risks: when statistics can’t predict the future (The Guardian 9 JUN 2013):

False positives are common for the simple reason that if you test a million healthy people, even with a 99% accurate test, you will still have 10,000 wrong results. And that’s not including human error. Hopefully, you will not experience one of these:

5. Not the Full Story

TV Kills was the headline that raced around the world as a result of this study.

As New Scientist pointed out:

The asked 8800 people about their health, lifestyle and television watching behaviour, and then followed them over the next six years, during which time 284 of them died. Among people who spent more than 4 hours a day in front of the TV, it found, the risk of their dying within the period of the study was 46 per cent higher than among those who watched less than 2 hours a day.

The error is confusing CORRELATION with CAUSATION. The risk might involve the sitting rather than TV. Or it could be that those who sit in front of TV longer are not well.

THIS IS A COMMON AND DANGEROUS ERROR INVOLVING HEALTH STATISTICS

Now that we have more screening tools we must be more cautious.

Angelia Jolie had her breasts removed because of testing positive for the BRCA 1 and BRCA 2 genes, which are linked to an increased risk of Breast Cancer.

This is her decision. Anyone facing breast cancer would seriously consider this option.

BUT, be wary if you face this decision.

Think of Asthma. If we started our research into asthma looking for asthma genes we would have found them.

Genes create a pre-disposition for Asthma (hence the correlation) but they do not cause asthma.  The dust mite, pollen, cat, dairy and other allergies cause asthma. If researchers had concentrated on genes alone our knowledge of asthma would be limited.

 Another study showed that 80% of prisoners in Australia smoke. Isn’t it obvious? Smoking causes criminal behaviour!!!!!