Between last Thursday and this morning I realized that two of the problems in the text are problematical. One is marked “complex” and I told them not to try it. One I asked them to do turns out to be impossible in an interesting way.
I think I can build an interesting class on these two problems, pointing out that often enough the numbers in the newspaper actually don’t make sense.
But do I want to build that class? It’s a digression that comes at the right time in the classroom dynamics, but at the wrong time in terms of “covering the syllabus” – that would call for linear equations, functions, scatter plots in Excel. Perhaps I can do both.
Here’s the problem with nonsensical averages:
Wal-Mart will pay $40m to workers
On December 3, 2009 the Boston Globe ran a story under that headline that said (in part):
Wal-Mart Stores Inc., the world’s largest retailer, has agreed to pay $40 million to as many as 87,500 current and former employees in
Massachusetts, the largest wage-and-hour class-action settlement in the state’s history.
The class-action lawsuit, filed in 2001, accused the retailer of denying workers rest and meal breaks, refusing to pay overtime, and
manipulating time cards to lower employees’ pay. Under terms of the agreement, which was filed in Middlesex Superior Court yesterday by the employees’ attorneys, any person who worked for Wal-Mart between August 1995 and the settlement date will receive a payment of between $400 and $2,500, depending on the number of years worked, with the average worker receiving a check for $734.
www.boston.com/business/articles/2009/12/03/wal_mart_will_pay_40m_to_workers/
What can “average worker gets $734″ mean?
The mean is $40 million/87,500 employees = $457/employee.
A little thought shows $734 can’t be the median – if half get more than that and the minimum is $400 then the mean would be at least
(400+734)/2 > 457.
I suppose the mode could be $734, but only if the distribution were very peculiar, with that value just happening to be more common than
any other (but not very common). I can’t believe that was what was meant.
Perhaps the answer is in “as many as 87,500″ workers, where the actual number is a lot smaller, making the mean larger.
OK – having written this much in the blog before the class, I’ve pretty much committed to working on it in the class. I’ll report back on what happened …
Wednesday evening – at least I’ve updated this post before tomorrow’s class.
We did work on the fact that the averages in the article made no sense – $734 couldn’t be the mean. When I returned to the CSM manuscript to update the problem and provide a solution I discovered that the numbers are even more nonsensical. It turns out that there’s a $12.5 million lawyers’ fee to come out of the $40 million, which leads to a mean much less than the $400 per worker minimum. There’s no way to make sense of these numbers.
I asked the class whether this had been a good way to spend class time, and, if so, why. One student gave what I thought were two good reasons. First, that it was a lesson that showed that the numbers in the paper can be just plain nonsense, and second it was a good context in which to review the meanings of mean, median and mode.
We spent a little time on the Lahey clinic ad saying that it (the clinic) was one of nine hospitals where patient heart attack survival rates were better than average – possible if the average is the mode or the mean, but only if the distribution is very strange.
Limited time in the last third of the class to introduce linear functions – electricity and cell phone bills, car rental. Just the shape of the formula
fixed cost + (rate)*(amount used)
Tomorrow I’ll do linear equations in Excel. Introducing the scatter plot (picture of a function) is at least as important as the formula.
blog home page