Math — Applications for Living V

The class (Math119, called “Math — Applications for Living”) is now covering quite a bit of statistics, and I thought I would share a problem from yesterday’s class that incorporates ‘measures of typical values’ (aka ‘average’). 

So, here is the situation described:  “A small local company has 8 workers, and here are their hourly rates of pay:   $9, $9, $9, $10, $11, $18, $36. What is the average hourly pay?”

In this case, I had students work on this problem in pairs; they had directions for finding the mean, median and mode.  The big question was “Which average reflects ‘typical’?”

This was a good situation to show the weakness of the mean as an average or typical value; those outliers create false impressions.  The group actually thought that the mode was the best average because 3 workers had this pay … even though it was the lowest.  Numerically, the median was the best and we talked a bit about the pros and cons of each average. 

Essentially, this work on the ‘average’ supports the cynical statistician view of the world — we don’t have the answer, all we have are hints at something that might (or might not) be true.  Fortunately, this same class gave a chance to talk about distributions of data, and begin ‘distributional thinking’.  The students got the idea that we should try to represent a set of data with one number.

Some students in class had already noticed that the median was used for some things (like home prices, and the net wealth discussion — see http://www.pewsocialtrends.org/2011/07/26/wealth-gaps-rise-to-record-highs-between-whites-blacks-hispanics/).  It was also clear that the word ‘average’ used so often does not state which one — too often, it is the mean (as in ‘the average number of televisions per household is 2.4’).

The class is going to move on to other statistical topics, some of which have more exciting uses in life.  The one above might be of interest, or at least be enjoyable to read.

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3 Comments

• 

  By Peter Brown, February 25, 2012 @ 8:42 am

  Big difference in how this is taught by us typically. We usually teach this with a close eye on pen and paper manipulations of addition and division. Ugh. Here is a topic I would love you to muse on- one that we had a long discussion on. “The purpose of a math class is to prepare you for the next math class”.

• 

  By Jack Rotman, February 25, 2012 @ 4:18 pm

  So true, Peter. We often cover ‘averages’ and some ‘statistics’ in a pre-algebra (or arithmetic) class — though the only real outcome is that students need to identify directions that call for them to do particular operations. Not much is usually said about the reasons for using the mean as the average, nor the reasonableness.
  In terms of purposes for a math class, there is the ‘prepare you for the next math class’. For this topic (average), it relates to another goal — “appear to justify procedural content by inventing problem situations which result in performing those procedures”. Too often, geometry and statistics are used in a math class for this second purpose.
  Thanks for the note; I may ‘muse’ further on this 🙂

• 

  By Kathy Almy, February 27, 2012 @ 12:51 pm

  Agreed. One of the things I like most about the MLCS course is that there is value to the students right now. The goal is not just to be ready for another course, it’s also to gain skills and understanding that can a help in their life and work while they’re in the course. That type of realism and usefulness is very motivating most learners but especially the developmental one.

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