Unit 5: Distributions and the Normal curve
Read chapters 16, 5, 17, and 18 (in that order) in the text.
1) From the book:
Chapter 16, pages 285-286: 1-4, 6-8, 10
Chapter 5, pages 93-96: 1-4, 8, 9, 11
Chapter 17, pages 304-306: 1, 2, 4, 7-9, 12
Chapter 18, pages 327-329: 2, 4-7, 12-14
Rick Weiss and Ka Leo O Hawaii, "Class status linked to
determining of IQ", University Wire,
Sept. 10, 2003.
Available from LexisNexis
Note: You may experience a browser crash with Safari
on a Mac. Try Firefox if you have problems.
Use the following to search:
Text Box: Class status linked to determining of IQ
Source: All News (English, Full Text)
Date: Previous 10 years
Possible essay questions
Remark: A common IQ test produces scores that
follow a bell (Normal) curve
with average 100 and SD 15.
Here is an online IQ test.
- The article discussed, briefly, the controversial
book The Bell Curve. This book, in particular,
stated that blacks have lower IQs, on average, than
whites. It went on further to say that this difference
will eventually cause racial stratification and
a resurgence of racism. The book authors' argument
relied on IQ being genetically determined.
How would you use this article to discount
The Bell Curve's conclusion.
- Given that children from very low income
homes score low on IQ tests and that improving
their environments will increase their IQ scores,
the average IQ of the entire population will
increase. What will happen to the SD?
- The article states that
University of Minnesota behavoiral geneticist Irving
Gottesman "noted that [IQ] remains the best predictor today of
social and economic success in U.S. society."
Argue that the correct statement could be
social and economic success in U.S. society is the
best predictor today of IQ.
This week we work with payroll data (total of the
players' salaries on a team) for 2007 Major League Baseball teams.
Before you do any computations with Excel, what percent of teams
do you expect to have below-average payrolls? And what percent of teams
do you expect to have payrolls below the median? Do you expect the data
to be normally distributed?
Now, suppose the data is normally distributed. What percent of the teams
would have salaries below the 84th percentile? What value would
the 84th percentile be for a normally distributed dataset with
average $82.63 million and an SD of $33.35 million?
On the Computer
Copy the 2007 baseball payroll data below into a spreadsheet program:
Baseball payroll (salaries-only list): Move these into the spreadsheet.
If you have trouble with the spreadsheet program, consult the supplement
Using Excel 1:
- Create a histogram for the payroll data using
class intervals of length $20,000,000,
up to $200,000,000.
- Compute the value of the average, median, mode, 84th percentile
and standard deviation for the salaries. (The Excel function for what we
call SD is "stdevp" [the "p" stands for population]. The function "stdev"
gives what we will later in the course call "SD+", the "sample
standard deviation".) Which team would you say lies in the
- Determine the percentage of teams with below average payroll.
- Compare the actual data with your predictions. Is payroll data for baseball
players approximately normally distributed? Would you say
that the payroll data is symmetric,
left-sided, or right-sided. Does the rule, the average
follows the tail seem to be valid in this situation?
- Find the correlation coefficient between payroll and number
of wins. How would you describe the correlation?
- Create a scatterplot for payroll versus number of wins.
Let payroll be on the x-axis.
use of the correlation coefficient valid, based on your
scatterplot? While you're at it, insert the regression
line in the scatterplot.
- What would you predict for the payroll of a
team with 88 wins? There are 3 teams with 88 wins.
Which teams comes closest to your prediction?
- There seems to be one outlier in the scatterplot. Remove
this data point and recalculate the correlation coefficient.
What do you get? Did the correlation coefficient change in
the way (both in size and direction) you expected? Explain.
Last revised February, 2008. Mail to
Copyright 2008 © Colgate University. All rights reserved.