Archive for the ‘Averages’ Category


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



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!!!!


DAY 500 COVID-19 … some curious stats

June 7, 2021

Mathspig has tracked the Covid 19 Stats through the Worldometer tracker and calculated the AVERAGE NO. DEATHS per day at the 50607080, 100 , 200 DAY and the 1 YEAR mark ..

and now at the 500 DAY mark.


Note: Approx 1/3 of deaths around the world are due to accidents, diseases other than Covid, or suicide.


Vaccine math. Results vary because …

March 26, 2021

According to the AstraZeneca Media Release, 22 March 2021, “The AstraZeneca US Phase III trial of AZD1222 demonstrated statistically significant vaccine efficacy of 79% … based on 32,449 participants accruing 141 symptomatic cases of COVID-19. The trial had a 2:1 randomisation of vaccine to placebo.”

A careful review of all available safety data of more than 17 million people vaccinated in the European Union (EU) and UK with COVID-19 Vaccine AstraZeneca has shown no evidence of an increased risk …”


The Washington Post, 25 MAR 2021

An updated company analysis of the coronavirus vaccine developed by AstraZeneca and the University of Oxford showed that the two-shot regimen was robustly effective — 76 percent at preventing symptomatic illness — according to a news release from the drugmaker late Wednesday.

Among people 65 and older, the vaccine was 85 percent effective, the company reported.

New York Times, 9 APR 2021

UK plus & 30 EU countries have administered 34 million AstraVeneca doses and report a blood clot condition in 222 patients and 18 fatalities. 

Risk Factor for blood clots = 1: 153,000 

Risk of death ~ 1: 2,000,000

Many countries including Australia advise the use of the AstraZeneca vaccine for the 50+ age group as the blood clot condition appears mostly in younger patients.


1 Year COVID-19 … some curious stats

January 22, 2021

Mathspig has tracked the Covid 19 Stats through the Worldometer tracker and calculated the AVERAGE NO. DEATHS per day at the 50607080, 100 , 200 DAY mark …

and now at the 1 YEAR mark.




New York Times article here.

BBC article here.


DAY 200 Covid-19 .. some curious stats

August 8, 2020

Mathspig has been tracking the Covid 19 Stats through the Worldometer tracker and calculating the AVERAGE NO. DEATHS per day at the 50, 60, 70, 80,, 100 and now, the 200 DAY mark. The average is still rising which, as the average started low, is not good news. What can I say? Mask Up, folks. 

MATHSPIG is reporting in from lockdown in MELBOURNE, Australia, where mask-wearing outdoors is now compulsory, there is an 8pm-5am curfew and travelling more than 5km from your residence is banned.


Cars in the USA are how old? Really? No way! Look at the World and Do the Math

February 3, 2018


The average age of the 60 years of FORD vehicles here is 30 years. MODEL NAMES at end of post.

I did this to show that averages can tell us a lot or, in this case, not very much.

Here are some averages that tell us a lot about different countries and their love of cars!

The average age of vehicles in USA is a record-high of 11.6 years. More here.

Car ownership rates data here.

This is the average vehicle age, which includes vans and utes. Almost 1,000,00 vehicles were scrapped in 2015-16. More than 30% of vehicles are less than five years old. Data here.

In 2016, the average age of vehicles on Canadian roads was 9.66 years. Data here.

The average age of cars in UK is 7.7 yrs. some interesting stats here.

The average age of vehicles in New Zealand is 14.3 years. The average age of trucks and buses is over 17 years. Data here.

Cars in the European Union are on average 10.7 years old. Data here.

The average age of vehicles in Poland is 17.2 years. Daata here.

The average age of vehicles in Romania is 15.3 years. Data here.

The average age of vehicles in Greece is 13.5 years. Data here.

Ethiopia has the lowest car ownership in the world with 2 per 1,000 inhabitants in 2014.

The average age of Ethiopia’s fleet is 15-20 years. Best guess! Data here.


Dangerous Maths 2: Death by Snake, Spider, Quad bike, Kangaroo, Raccoon and Vomit

August 7, 2015

This post is really a PR exercise for sharks. We fear them. We’re horrified by the thought of being eaten alive!!!. We only have to hear the sound track from JAWS to feel the fear.

Why do we fear sharks? Look at the numbers. REALLY. Show your students. What about stairs??? Quad bikes? Chairs? Bees? That’s when you should feel the fear!!! We are irrational beings. This is why we need maths. We can make rational decisions using maths. There is also a safety message here. The maths speaks for itself. We won’t hammer it.


There is lots of maths you can do with these tables.

  • Bar Graphs
  • Pie Charts
  • Ratios (What’s the ratio of death by Snake to Quad Bike?)
  • Fractions (Show death by jet ski to falling down stairs as a fraction)
  • Percentages
  • Powers to the base 10. How many deaths occur in each country per 100,000 or 1 x 10head of population for, say, Quad bikes or ATVs? We can use these numbers to compare death rates and find out how dangerous riding a Quad bike is in each country.

……..Population Data

……..Aust…23 million = 23 x 106

……..USA…319 million = 319 x 106

……..Canada…35 million = 35 x 106

……..UK…64 million = 64 x 106

But we’re doing this for the SHARKS!!! Death Australia Mathspig

  1. Cyclists. 2. emergency lanes 3. fell off a chair 4.QUAD BIKES. 5. Horse, donkey. 6. buses 7. Cow, bull. 8. ice skates, skis or skateboards. 9. Venemous snake 10. kangaroo 11. bee 12. emu 13. Jet ski 14. Shark 15. Crocodile

Death USA Mathspig 21. Quad Bike or ATV: In 2007, 107 children younger than 16 were killed on ATVs. 2. Cyclists 3. choke on vomit  4. Cats, cows, horses, pigs, raccoons. 5. Bees, wasps  6.PWC or Jet Ski 7. Lightning 8. Xmas tree fires 9. Snowboard 10. Venomous Spider  11. Scorpions 12. Venomous Snakes , lizards. 13.Crocs & gators  14. Shark Death Canada Mathspig

  1. ATV Quad Bike 2. Canoe  3. Kayak 4. PWC or Jet Ski  5. Unpowered inflatable 6. Avalanches or landslides. 7. Lightning 8. Toboggan 9. Moose –Car collision 10. Bears (All Nth America) 11. Rattle Snake 12. Wolves 13. Shark

Death UK Mathspig

  1. falling down stairs.  2. Cyclists.  3. Choke on vomit   4. Falling off Chairs 5.  QUAD BIKE or ATV 6. Buses 7. Struck by cow, horse, other mammal 8. hornets, wasps, bees. 9. PWC or jet ski .10. Parachutists. 11. Skateboards, ice skates, skis 12. Canoe. 13. Shark 

MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue

July 10, 2015

Mathspig m&m maths intro

Hellooooo My Little Sweeties,

There is so much maths you can do with m&ms, it’s hard to believe there is any other sort of maths.

You can study:

Countingtimes tables, set theory, Bar graphs, Fractions, % and decimalsMean, median, modeand parabolas (using a really cool peg-powered catapult).

But my favouritest ,developed by Patrick Len, is using m&ms to demonstrate half life in radioactive substances and therefore write an exponential equation.


m&ms  table

Throw a fixed no. m&ms on a table. Mathspig chose 128 m&ms for a very good reason. Eat the ones with the m showing. Count remainder. Throw again. Eat the ones with the m showing. Count remained. Keep doing this. You will end up with results like the following. (Not identical as chance is involved)

mathspig   m&m maths exponential fn  2

Wow! m&m’s and exponential equations. How yummy is that!!!!!!

More yummy maths:

m+m maths 1: find the volume using m+ms!

m+m maths 2: Guess, NO, calculate the number of m+ms in a jar!

m+m maths 3: how many m+ms will kill you?

m+m maths 4: How many m+ms will kill my dog?

m+m maths 5: how many m+ms will kill my cat?

m+m maths 6: How many m+ms will kill my pet rat?

m+ms maths 7: how many m+ms will kill my pet mouse?

Mmmmmmm! Can’t talk. Face full of chocolate.

Bye bye



Maths Mystery Box 1: Not Stupid

April 10, 2015

Maths Mystery BOX 1

Not stupid. Just, like, lazy.

Mathspig averages quote

I use the quote above to explain to people that Averages don’t mean much. This is a typical response. Really! Wow! Australians have one breast and one testicle!

We live in a culture of Selective Stupidity. Most people can do the basic maths of: + – x % $$$$, but many don’t bother. We leave maths thinking to machines and their algorithms.


So you buy 4 choc bars at 50 cents each and, for fun, ask the shop assistant ‘how much?’ They work the answer out on the cash register. They have to record the purchase. Still, how hard would it be to say $2? We don’t even try.

Yet we need maths every day to buy stuff, read timetables, pay bills, cook, understand food labels, take medication and more. Maths is used in sport, driving, gaming, gambling, drinking (ie. alcohol levels) and banking; maths is used in the workplace, the law, politics, advertising, fitness, the travel industry, gardening, the music industry (Royalty payments are a big issue now), watching TV (Download speeds are crucial), Facebook (How many likes?) and more.

The UK maths-promoting charity National Numeracy quotes from research suggesting ‘weak maths skills are linked with an array of poor life outcomes such as prison, unemployment, exclusion from school, poverty and long-term illness’. (Judith Burns, Poor numeracy ‘blights the economy and ruins lives‘, BBC News, 5 March 2012)

Yeah! And ….

Mathspig hot date quote

Josie Gurney-Read in an article Damaging maths mindset holding pupils back,( The Telegraph, UK, 30 Oct 2014) claimed 17 million adults in the UK have poor maths skills and this is costing the economy £20 billion a year.

£20 billion,eh?

The previous article by Judith Burns, above, quoted research by KPMG auditors that put the annual costs of poor numeracy skills in the UK at £2.4bn.

So £2.4 billion, is it?

Who’s doing the Maths HERE?

Who cares? We let these numbers just fly past without thinking about them. We choose to suffer from Selective Stupidity.

To challenge middle school students to think about the numbers they read here are a few tricky questions:

the maths quiz

Look at the following questions and see if you can work out why the maths is totally dodgy.

1. Dumb and Dumber

doll solar

Solar Plus claimed, after a survey of 60 customers, that 99.98% of customers would recommend their product.

What’s wrong with their Maths?

Answer here.

2. Wanna get rich? Look at the Graph, Dude!

Financial advisers around the world wheeled out graphs like the one below to show that investing in the stock market is very secure and that down turns in the market in 2007 were minor. Oh Yeah!

What is wrong with this graph!

Mathspig Maths Mystery Box 1 graph

Answer here.

3. Run a Red Light. 0.9 sec! $234 fine! Is that fair?


Look at the maths. How far would a Mazda 3 travelling at 60 kph (37.3 mph) travel in 0.9 seconds? 

Ans here.

4. Can you out run a fireball?

This is a Movie Cliché we see over and over. But is it possible?

Maths Mystery Box 1  outrun fireball

A Fireball travels at 400 m/sec. That’s metres/sec. Now can you do the maths?

Answer here.

5. You could win the lottery! The least drawn numbers are ….


If the least drawn numbers are 41, 32, 10, 43, 35 and 20 will picking these numbers improve your chances of winning the lottery?

Answer here.

6. The Equation for the Funniest Joke is:

According to The Telegraph UK the formula for the funniest joke is:

x = (fl + no ) / p


x = funniness of joke

f = funniness of punchline

l = the length of the build-up

n = the amount some falls over

o = the “Ouch” factor of physical pain or social embarrassment

p = power of the punchline

So, what’s wrong with this equation? Ask Weird Al Yankovic.

MAD Magazine Weird Al Marker Tooth_54dce7ae29a8f0.26429747

Ans here.

(Quick Ans: It’s all rubbish. Guess work x cow manure = bulldust. You cannot measure any of these variables. What’s the unit for measuring funniness?)

7. Coconuts kill 150 people a year. Does that sound right?


OK. You are not a crazy death-by-coconut research scientists. But have a guess. Are coconuts that dangerous?

Answer here.

8. 9 out of 10 serial killers prefer murdering kids with Emo hair.


Does this sound reasonable?

Answer here.

Quick Answer: There’s a lot of joke maths out there but some folk take it seriously.


Maths Mystery Box 7: PHONES

February 18, 2015

Maths Mystery BOX 7

Middle school maths challenge

Algebra & texting

or  LGbra & txtN

According to a Nielsen Survey the Average US teen sends 3,000 txt messages a month. Averages don’t tell us very much. As this fab post at Maths PLUS explains. The average number of ears on 5 people is 1.8 if one dude has one ear. The Nielsen study did show the averages by gender. Mathspig texting 1 Mathspig texting 2 Mathspig texting 3

This is the maximum cost per txt for pre-paid phone cards. Anyone who sends this many txt messages a month would be crazy if they didn’t use a monthly phone plan.Mathspig texting 4 Mathspig texting 5


Mathspig texting 6

Some txts are serious. Very serious.

The 24/7 CRISIS TEXT LINE in the USA has helped many teenagers in crisis.

The phone no. in the USA is


the numbers down the Left of the phone.

OR from outside USA add code here. You can find details of the Crisis TEXT LINE in R U There? By Alice Gregory, The New Yorker (9 FEB 2015)


Ha Ha!

Some txts are NOT serious.

Texting Boredom Mathspig 7

Would you pay for this?

Mathspig texting  8