I have a problem that I want to pose to my Statistics students, and if you are reading this, I would love to get some feedback in the comments section.
Prior to this activity, students will have studied:
– Mean, Median, Mode, Range
– Standard Deviation of a population, (but not a sample)
– Very brief references to normal distribution
– Correlation coefficient
– Linear regressions, and some curve-fitting.
I would like to use this to reinforce measures of central tendency, and also as a jumping off ground for box-whisker plots and the interquartile range, and standard deviation of a sample. As well, I want to get to normal distributions in more depth.
Let me provide the problem, and then you’ll see some questions at the bottom:
WHAT EXACTLY IS “MIDDLE CLASS”?In a recent interview, Romney commented upon the middle class, in talking about his tax plan. From the San Francisco Chronicle:Romney’s comments came an interview broadcast Friday on ABC’s “Good Morning America.”“No one can say my plan is going to raise taxes on middle-income people, because principle number one is (to) keep the burden down on middle-income taxpayers,” Romney told host George Stephanopoulos.“Is $100,000 middle income?” Stephanopoulos asked.“No, middle income is $200,000 to $250,000 and less,” Romney responded.His campaign later clarified that Romney was referencing household income, not individual income.
- The data in the first sheet is made up. All I had was the US Census data, not individual household data – so I used the randombetween function in Excel to generate the incomes, so that they will average and distribute in the same way as the US Census information. So the data is representative of US data, but not actual data. How do I communicate this to the students? Is the above description ok?
- Thoughts on taking this to normal distribution? The data is not at all normally distributed.
- I hope that students will be able to at least sort the data, find mean (around $71,000), median (around 50,000), and std dev (around 81,000. Yikes!). Because of the huge size of the std dev compared to the mean, students will not be able to say, “A typical range of incomes will be the mean plus or minus the standard deviation” with much meaning, since the mean minus std dev gives someone negative income.
- Any other thoughts that occur to you as you look at this would be great.