In this course we will pay attention to the numbers that we see in daily life. For today, that meant looking at today’s copy of The Boston Globe and taking the time to think about the numbers. I handed out copies of the paper, put students in groups, and asked them to find an article that used quantitative information. We went around the class talking about the information and the context.
It’s always a gamble to bring in copies of the paper and hope that there will be enough interesting and relevant articles. It worked out fine today and we found a good number of different examples of quantitative information. Without any planning on my part, most of the examples pointed to topics that we will cover soon, such as estimation, percentages, and averages.
The article that we spent the most time on was the article about “Fed Up Flyers”: http://www.boston.com/business/articles/2011/01/25/complaints_grow_from_fed_up_fliers/
What was fun – and surprising – was that we found a mistake in the article. An airline analyst is quoted as saying “If you have a 90 percent load factor and you cancel a flight and the next flight is 90 percent full, it’s going to take you an additional 10 flights to accommodate the passengers on that one canceled flight.” We talked about what “load factor” means (and how sometimes we’ll need to look up definitions to really understand information) and did an example of a plane with 100 seats and a 90% load factor. That means that 90 of the seats are taken. If that flight is cancelled, and if the remaining flights are 90% full, then it will take 9 flights to accommodate the remaining passengers. We can see this by pretending all the planes hold 100 people. Then the 90 people from the cancelled flights will fit on the next 9 planes, 10 people at a time. The Globe said it would take 10 planes, so it was interesting to see that error.
There were some complicated graphs that we discussed, including a graph of daily temperatures in January. The graph had a lot of information: “normal” highs and lows (which we decided meant “average”), highs and lows from 2010, and record highs and lows. We saw that it was warmer than usual at the beginning of January, but colder than usual near the end of January. Interestingly, the article didn’t really refer to the graph. Instead, the reporter compared our temperatures to temperatures in Canada and Siberia. It would be a good exercise to study the graph and write about how cold it really has been, compared to “normal”
The main tools we used today were estimating and rounding. To check some of the figures from the articles we rounded the numbers and did some arithmetic to make ballpark estimates. The examples and homework for Chapter 1 will give you good opportunities to practice this; it’s a skill (actually, a habit) that we hope you’ll use throughout the semester.
I started with the same Globe and ended up in entirely different places. I asked them to find articles with numbers that were not straightforward (so not the temperature graph on the front page – good for data visualization but not for Fermi problems) and not impossible complex – to look for some that they found confusing but thought they could understand with help. I also suggested they skip the sports section (for now – students can come back to it at term paper time).
First we discussed an ad from Sovereign Bank for
Home equity loan at 2.25% APR for the first six billing cycles.
We spent a lot of time on the vocabulary. In particular, we talked about the difference between a home equity loan and a mortgage, what “collateral” meant, how the value of your house (your collateral) and your credit rating might influence the interest rate: the more likely you are to be able to repay the loan the less interest the lender needs to charge you. I showed them in the syllabus that we would study borrowing and interest rates in a month or so.
One student knew that “APR” meant “annual percentage rate” but was puzzled – how can you have an annual rate for just six months? When I asked if you could drive at 60 miles per hour for just half an hour she got it – adding “but you wouldn’t go 60 miles”. So we had a (very brief) exposure to rates and units.
Then we moved on to
The government says it will sell 465.1 million warrants it holds from Citigroup Inc. in an auction today. It is the latest effort to recoup costs from the $700 billion financial bailout.
For 255 million warrants classified as “A warrants’’ the minimum bid price will be 60 cents. The second group of “B warrants’’ will have a minimum bid price of 15 cents.
Everyone knew what US and Citigroup were. Some knew what a warrant was (not an arrest warrant) – but all we needed to know was that it was something that could be bought and sold. The natural question was “how much of the $700 billion bailout cost does this amount to?” The answer “not much” is too qualitative – to find a better answer we need to work with the numbers.
Then the fire alarm bell rang.
Here’s what I would have prompted for:
The 255 million class A warrants at 60 cents each will bring in a minimum of about
$250,000,000 * 0.60 = $150,000,000
(rounding the 255 million to 250 million so I can do the arithmetic in my head).
There are then
465.1 million – 255 million ~ 200 million
class B warrants – again rounding so I can do mental arithmetic. These bring in 15 cents each, for a total of $30,000,000.
(I might have taken the time to point out that dealing in cents rather than dollars is actually dealing in percents – 15% of 200 is 30.)
So this warrant sale will bring in about $180,000,000 .
To compare that to the $700 billion bailout cost we should divide, not subtract. To find
180 million / 700 billion
note that 180/700 is about 4 and million/billion leaves three zeroes in the denominator, so the answer is approximately
4 / 1000 = 0.004 = four tenths of one percent.
Truly not much – even if the warrants end up selling for, say, two or three times the minimum!
Maybe the class will read this – I told them about the blog. (Extra credit: if you read this, write me email or comment here telling whether you understood it. The extra credit is for the reading and writing, not the understanding.)
Maybe I will do this in class next time (if no snow day), maybe I will assign it as a problem. Either way I’ll put it in the book.
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