Homework on the Big Picture
These apply to everyone, future teachers and others. Feel free to copy and paste, but do think about the
answers as you go.
1. What are the categories in Bloom's Revised Taxonomy?
2. What are the 8 Standards for Mathematical Practice?
Chapter 01.01 Homework
If you are a future teacher:
Write a description of the GEICO activity, detailed enough that you could give it to a friend who was not
in our class and they could lead a class through it. Include the proper vocabulary. Also include the
rationale for the various things I said, did, or chose.
Do not worry about the format of your description--some people have taken a class that teaches them a
lesson-plan format, and others have not, so I do not require it as a format. Do not spend time on things
in the lesson-plan format that aren't relevant to learning statistics.
If you are not a future teacher:
(in these dot plots, do not worry about stacking dots in the case of ties. There won't be any ties worth
worrying about.)
1. Do a simulation of the GEICO activity using software. Use a class size of 20 students.
a. Do a dotplot of the "savings" amount
b. Report the average "saved" by the whole class, as if everyone switched.
c. Report the average saved by just those with a positive savings amount.
In Excel, I would use the following functions: RAND(), SUMIF(), and COUNTIF(). For example,
=SUMIF(B11:B30,">0") will sum those items in that range that are greater than 0.
Excel 2007 and later should have an "averageif" function that can save you some time. It seems
that the Google Docs spreadsheet does not have it, though.
2. Now repeat that 100 times and record the results of each trial. Do two dot plots of the results:
the whole-class averages on one, and the just-those-who-would-switch averages on the other.
3. Now change the class size to 40 and repeat 100 times, and again do two dot plots of the results.
4. Comment on how the 20- and 40-student class sizes in questions 2 and 3 compare to each
other.
Chapter 01.03 Homework: Measures of Center
We are deliberately skipping all parts involving trimmed means.
1.1
a) Sample size?
b)Sample mean?
c)Sample median?
d) Paste your dotplot here:
e,f) skip.
1.2
a) sample mean and sample median?
b) skip.
c) paste your dot plot here:
d) using only the mean & median (not the trimmed mean), do you have evidence of outliers? Explain.
1.3
a) paste your dot plot here:
b)
c)
d)
1.4
a)
b)
1.5
a)
b) mean and median, but skip the trimmed mean.
c) again, do the mean & median parts, but skip the trimmed mean.
1.6
a)
b)
c)
d)
Question A:
A report in the Wall Street Journal says:
" The Schwan Food Co. [has] 6,000 roving sales people deliver frozen products to homes of three million
customers across the country."
If you compute 3 million / 6000, is that a mean or a median? What are the units?
http://online.wsj.com/article/SB10001424052970203462304577138961342097348.html
Question B:
The data in this problem are made up, but are somewhat realistic, and describe how Social Security
taxes roughly work in the US.
Suppose the mean household income is $60,000/year, the median is $50,000/year, and the mode is
$44,000/year. Suppose there is a 10% tax on all income, and there are 100 million households. How
much money does this tax bring in per year? Explain your reasoning.
Question C:
Again, these data are made up, but are somewhat realistic, and describe how property taxes roughly
work.
Suppose that the mean house value is $120,000; the median is $100,000 and the mode is $75,000.
Suppose there is a 2% property tax, and there are 10,000 homes in a city. How much money does this
tax bring in for the city, per year? Explain your reasoning.
Question D:
Thinking back to Questions B and C, explain when to use the mean and when to use the median.
Question E: (optional)
Write a similar question about the mean, median, and mode of the baggage weight per person on an
airplane. Use realistic numbers. Or use any other real-world scenario that interests you, or that you
think would interest K-12 students.