But Baby, my Feets too Big!!!!!

Those Hippie Statisticians at The Australian Bureau of Statistics (ABS)  are Navel Gazing Again!!!! . Here are the statistics for the height of students belly buttons above the ground for Year 4 – 12 students. ABS  #mce_temp_url#

 

 

 

 

 

 

 Stop!!! WARNING!!!

Before we do any maths with students height mathspigs, be warned. Students can be teased or embarrassed by their height. Mathspig has always argued that a lampost is tall but does not have much of a personality. And a bee is very small but you’d be crazy to tease one. Nevertheless we will use celebrity heights and average student heights instead. 

Here we go!!!!!

 

 

 Q1. DO YOUR FEET GROW AT THE SAME RATE AS YOUR HEIGHT?

 Look at the data. It is useless. THIS IS THE POINT. You have to make sense of data not just sprout numbers. Foot sizes actually shrink!!!! There is insufficient information. The ABS random sample size used was too small. So baby your feet might be too big… but we can’t tell from this data.

 

 

 

 

 

 

 

 

 Q2: Does the ‘average’ Aussie student have divine proportions?

 The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci around the year 1487. This sketch supposedly represents the perfect proportions in man. Measure Height and Belly Button Height of Vertruvian man. Divide his Belly Button Height by his full height.

We will call this the DIVINE FRACTION. 

How do Aussie Students compare? You have the data needed to calculate the DIVINE FRACTION for each year level.

 

 

Q3: How do the average heights of our  students  compare to students in other countries?

If we could took a very, very large number of student heights they would produce the graph below. It is a NORMAL DISTRIBUTION or A BELL CURVE. The curve below is for young adults in the USA. We do not know the actual number of students for each height.  

ADVANCED MATHSPIGS; You will find more data, a cute bar graph using students  and some interesting bimodal graphs (combining the Bell Curves for Female and Male heights) @#mce_temp_url#

How do Aussies compare? See the graphs below. We do not know how many students are involved. We can only say  our average Year 12 student is taller than the majority of their students!!! Ha! HA! If, that is, the data is reliable and the foot sizes suggest maybe NOT.

 

 

 

 Q 4:  How does the average height of  Aussie students for each Year level compare with celebrities? 

The pics and some stats come from The Sunday Age ( Coming Up Short 13th Sept 2009) . Here are some celebrity heights:

Lou Reed, Rock Star    1.65m

Nicolas Sarkozy  French President  1.65m

Napoleon   1.68 m

Syvester Styllone Actor 1.70 – 1.79m (No one is sure.)

Andrew Bogut, Aussie Basketball Champ (Pictured) now playing for the Milwaukee Bucks 2.13m

Tom Cruise, Actor  1.70 m

Katie Holmes, Actor  1.75 m

Nicole Kidman, Actor  1.79mm

Keith Urban, Singer   1.78 m

Aaron Sanderlands and Peter Street, AFL Players    2.11 m

Gary Ablett jnr, AFL Brownlow Medal Winner 2009  1.80m

Roger Federer, Tennis Star    1.85m

Michael Phelps, Olympic Swimmer   1.95m

Grant Hacket, Olympic Swimmer  1.98 m

Liesel Jones, Swimmer  1.78 m

Tyrone Smith, Rugby Union, 1.78 m

Digby Loane, Rugby Union   1.79 m

Cate Blanchett, Actor  1.74 m

More Maths. No Sweat!!!

 Mathspigs there are two things that stop kids doing maths. Fear & boredom. But we are going to show NO FEAR. You may find some of these equations a bit scary. I do too. But I can make some sense of some of this stuff. Here goes.

 The article No Sweat. Well, not as Much as You think (New Scientist 18/7/09 #mce_temp_url#  ) highlighted research by the US army into finding an equation for how much men and women sweat. They need this information so they can calculate how much water they need to carry. Makes sense.

 The full research paper by Sawka & Co can be downloaded for free from The Journal of Applied Physiology #mce_temp_url#  . 

 How do they calculate how much you sweat???

Basically, they use NUDE body mass work out how much weight you lose after exercise. Allowances are made for mass (or weight) by breathing in oxygen and breathing out water & carbon dioxide. 

They can also calculate how much heat is lost when you are nude if  m  ( or m with a little dot) is your sweat rate in grams per hour.

 

 

 

 

 

 Then things go a little crazy. Here’s one part of the equations for heat lost when dressed. I just want you too see how crazy some equations can be.  We’re not going to use it. But when you are doing studies like this you get used to such equations.

 

 

 

 

 

 

 

ARE WE SCARED, MATHSPIGS? No. We’re going IN to look at the results. We can make sense of them.

 

Thanks to Dean Van DEn Heuvel, Kyneton, Victoria for this fab math pig pic. We like happy mathspigs!!!!

 

When you read the table below keep in mind:

 

 

How much do you sweat????

Here’s your answer!!!!!!!

 

 

With one more piece of data you can calculate how much you would sweat in Battle Dress Uniform or body Armor plus vest. Your surface area:

“Normal” BSA is generally taken to be 1.73 m² for an adult. ( More @ Wikipedia: #mce_temp_url#)

Average BSA values
Child 9 years	1.07	m²
Child 10 years	1.14	m²
Child 12-13 years	1.33	m²
For men	1.9	m²
For women	1.6	m²

Which sport is more DANGEROUS to play? Cricket or baseball?

Mathspigs you are about to be hit on the head with some BALL PARK figures. There is so much maths involved in comparing cricket and baseball I hardly know where to begin. So I will just set you up with comparitive statistics for starters. Here they are:

 

 

 

 

You now have sufficient information to calculate the following:

Q1. If a cricket player  makes 4 runs (and runs between the wickets) and a baseball player hits a home run, who runs the furtherest?

Q2. What are the delivery ball speeds of an average pitcher and a mid paced bowler in m/sec?

Q3. How far would the delivery of an average pitcher and a  medium paced bowler travel in 10 seconds?

 Q4. If Shoaib Akhar fielded a ball in cricket 20 m from the wicket when the batsman was still 8m from the wicket (A typical running speed for humans is 32 km/h) would he be able to run him out?

 Q5. How long would it take a ball thrown by Joel Zumaya to reach the batsman if the pitchers mound was exactly in the middle of the baseball square?

 Q6. Which sport is more dangerous? We will base our calculations on the speed (or velocity) and the weight (or mass) of the ball. We must use the same units in all calculations. For each sport plot x-axis: velocity of ball (v) against y-axis mass x velocity (mv) of the ball. mv is the momentum. In ballistics the change in momentum is called the IMPULSE (impact for us). If you are hit on the head with a ball it is the change in momentum of the ball that does the damage. A small ball at a high speed can do as much damage as a larger ball at a slower speed. We are not including spin, curve balls or air resistance to keep calculations straight forward … literally!!! 

Now that you have your graph you can answer these questions:

Q6a. Which sport for professional players is the most dangerous? 

Q6b. At what speed does a cricket ball do the same damage as a baseball? Show three examples. (Hint: Draw a straight line from the Y-axis)

 

 

Pics: Tim Lincecum (Left) with 101 mph pitch, Shane Warne (Upper Right) and Shoaib Akhtar (Lower Left)