Discussion 1: Thinking about scale

Introductions

Each student shares:

• Name

• Class year

• Academic interest and/or major, if declared

• One fun fact

Numbers out of context in the news

For each selection, the student curator explains why they chose the example.

The class discusses the “three questions to put numbers in context.”

1. What is the context for this number?

   • What type of quantity is it? (An average? A percentage? A rate?) Would it be helpful to convert it to a different type?

   • What missing information would be helpful for understanding it?

2. What can I compare this number to?

   • Is this number large or small compared to other similar values?

   • Can I compare it to the past?

   • Is there a natural “denominator”?

3. What would I have expected this number to be?

   • Is the number surprising? Does it seem plausible?

   • Can I come up with a rough ballpark estimate?

Fermi Contest

Break up into groups of 2-3.

For each of the quantities below, come up with a ballpark estimate. You’ll have 15 minutes.

Then, enter your solutions into the poll:

For each question, the team whose guess \(B\) is closest to the true answer \(A\) on a logarithmic scale (minimizing \(|\log(A)-\log(B)|\)) gets a bonus point. (Why a logarithmic scale?)

1. How many pet dogs are there in North America?

2. How many hours per year does the average American spend sitting in traffic?

   • Is this a large number? Why?

3. How much would it cost to pay the tuition, room, and board of all Stanford undergraduates for 1 year?

   • What is this as a fraction of the University endowment?

   • Is this a large fraction of the endowment? What information do you need to know to decide?