michael shadbolt otumoetai college

Nine weird tips for adding

to level 2 and 3 StatsMichael Shadbolt

Otumoetai Collegemshadbolt@otc.school.nz

IntroductionOtumoetai College, State Co-ed in Tauranga. ~2000 students. 2IC Math Dept. 9 years teaching. L3 Statistics for most of that.

Standards realignment, full L2 Statistics course (no standards in common with our L2 Math course.)

As a result, we now have six L3 Statistics classes, without taking numbers away from the three L3 Calculus classes.

Q1. Why can incorrect Bivariate analysis kill

puppies?

Puppy Lives? You Decide!It’s not always obvious which variable is the response and which is

the explanatory. Sometimes we need to think about which one makes more sense as an explanatory.

Eg: Heart weights of puppies vs body weights of puppies.Do we want to be able to

predict a puppy’s body weight by cutting out its heart and weighing it?

Or do we want to be able to predict a puppy’s heart weight by weighing the whole puppy?

In this case, perhaps it would be better if heart weight was response and body weightwas explanatory…

I ruff you!

Q2. Why is freeze-dried ice-cream better than

cornflakes?

Continuity CorrectionQuestion: The weight of boxes of “Kellogg’s Kream Krunch”

are normally distributed with a mean of 760g and a standard deviation of 5g. If the weight of the boxes is recorded to the nearest gram, find the probability that a box of “Kream Krunch” is recorded as at least 750g.

Answer: If the box is to be recorded as at least 750g, the actual box must exceed 749.5g

Thus P(X ≥ 750) = P(X > 749.5)(continuity correction) = 0.98213

(note: without continuity correction, the answer would have been 0.97724)

750g

Q3. Why is goody-gumdropice-cream "poissonous"?

You Scream, I Scream…• You will be given a scoop of

gumdrop ice cream. • Eat it and count the number of

pieces of gumdrop you get. • The random variable X will be

the number of pieces of gumdrop per scoop of ice cream.

Q4. Why is Yoda a fan ofVenn Diagrams?

P(Try′) = 1P(Do) = 0.7P(Do′) = 0.3 P(Try) = Ø

P(Do)

0.7

0.3

?

P(Try)

Q5. Am I going to die froma meteor strike?

Meteor To Hit Earth!A meteor is going to hit Earth! We want to know the probability that it hits land, as opposed to landing in the ocean.• Why would we simulate this? (Why not do

an actual experiment?)• What tool could we use to simulate this?• What assumptions are we making?• How will we calculate the probability that a

meteor would land on… well, land?

Q6. Am I going to die froma lightning strike?

Fire Island Assessment

Sample of simulation outcomes (km2 lost)

Q7. Am I going to die fromfalling asleep?

Results from wearing a heart-rate monitor overnight. X-axis is time (seconds) after going to bed. Y-axis is heart rate in beats per minute.

Describe the overall trend. What would happen to Tim (the person monitored) if he kept sleeping? Make an approximate forecast for Tim’s heart-rate after 24hrs asleep.

Source: xkcd.com

Q8. Is Frane Selak the unluckiest man to ever live?

Q9. Are polar bears really stealing our money?

Area Bias Example:Polar Bear Population

• The World Wildlife Fund (WWF) has written on the threats posed to polar bears by global warming

• However, also according to them, about 20 distinct polar bear populations exist accounting for approximately 22,000 polar bears worldwide.• Only 2 of the groups are decreasing• 10 populations are stable• 2 populations are increasing• The status of the remaining 6 populations is

unknown• If you are only looking at the 2 groups

that are decreasing, it would be easy to say that the “Polar Bear Population is Decreasing”. You need to look at the whole picture to get the whole story