CHANCE News 5.01
(11 Dec. 1995 to 8 Jan. 1995)
Prepared by J. Laurie Snell, with help from William Peterson, Fuxing Hou, Ma.Katrina
Munoz Dy, and Joan Snell, as part of the CHANCE Course Project supported by the National
Please send comments and suggestions for articles to firstname.lastname@example.org.
Back issues of Chance News and other materials for teaching a
CHANCE course are available from the Chance Web Data Base.
Peter Doyle suggested the quote and comments that Bob Dylan also used it in one of
Somebody got lucky, but it was an accident.
Robert Johnson (Bluesman)
Concerning a question in the last Chance News Maya Bar-Hillel writes "The quote about
a person moving from state to state and raising the average IQ in both was made by
Art Buchwald, when the superintendent of higher education during Reagan's governorship, Max Rafferty, moved from California to Alabama." It is retold in Falk, R. & Bar-Hillel,
M. (1980), Magic possibilities of the weighted average, "Mathematics Magazine",
53, pp. 106-107. You can also find here an interesting discussion of the following
version of one of our favorite paradoxes.
Can you rearrange the population of the United States in such a way as to raise the
average IQ in all fifty states? If so, does this imply that you can increase the
average IQ in the United States but such a rearrangement?
Central Park's 22 inches not enough to win free car.
CNN News, Jan. 9, 1996
The owner of Potamkin Auto Center in New York said that they would pick up the cost
of multi-year car leases for anyone who leased a car from them between December 22nd
and January 2th if it snowed more than four inches in New York's Central Park on
Monday January 8th between the hours of 10 a.m. and 10 p.m. Well, it snowed 19 inches on
Sunday but, according to the national weather service, only 3.3 inches on Monday.
The owner said that he was insured and would have loved to lost the more than a million
dollars it would have cost him in return for the good publicity.
Do you think this would have been a favorable bet for the dealer if he had not had
Here are brief comments on three unusually interesting new statistics books.
Seeing Through Statistics.
by Jessica M. Utts
This book has as its aim that of a Chance course: to make readers better able to understand
and critically analyze current events in the news that depend on probability and
Utts discusses standard statistical concepts but always in terms of case studies reported
in the press or science journals. Emphasis is on basic concepts rather than on technical
considerations. Each chapter begins with a series of thought questions designed to get the reader started thinking about the topic of the chapter. Examples also
are centered around current studies, and each chapter has suggested mini-projects
relating to the topics of the chapter.
Dealing with current news events leads to a different emphasis from that of a standard
statistics text. More time is spent on topics such as: interpreting the results
of experiments, interpretations of probabilities, psychological influence on subjective probabilities, weather predictions, and economic indicators and their interpretations.
An "Instructor's Resource Manual" is provided, giving additional examples and the
author's goals for each chapter along with ways to achieve these goals. The manual
also provides other tips for how to teach this, admittedly challenging, new introductory
statistics course. The book is pleasantly brief, clear and a pleasure to read.
The Elements of Graphing Data.
by William S. Cleveland
This book is a significant revision of the author's earlier book and a companion to
his book "Visualizing Data". Cleveland discusses each principle of graphing data
in terms of an example from a scientific study. He gives details of the studies to
allow the reader to appreciate the significance of the scientific questions being studied.
Of course, my favorite was the graph of New Jersey lottery winners giving, for each
possible first digit of the number chosen, box plots for the amount the winner received. The more people who choose the winning number the less they get. Except for the
outlier corresponding to the number with all 0's, players did not like numbers beginning
with 0. Odd numbers were chosen more than even numbers and lottery players preferred larger first digits as suggested by the Benford distribution for first digits of
natural data. (See Chance News 4.10 for more on Benford's distribution)
Like Utts book, this is a wonderful book to read just as you might a novel. You will
never look at a graph the same way again after reading this book! In the current
issue of the Journal of the American Statistical Association, Robert Weiss has an
excellent review of this book, which also explains its relation to "Visualizing Data" (JASA,
December 1995, 90(432) p. 1488.)
Statistics: learning in the presence of variation.
by Robert L. Wardrop
William C. Brown, 1995
This is a non-traditional book for a traditional first statistics course. While giving
a serious discussion of statistical concepts, it does this in the context of current
studies and serious statistical research. The order of topics covered is very non-traditional and designed to allow the students to do their own experiments and analysis
almost from day one. The author uses previous student projects to illustrate basic
concepts throughout the book and as a source of many of the exercises. Not surprisingly these projects relate to questions of interest to students and should liven up the
book for other students. Again an enjoyable book to read whether or not you use it
as a text. An extensive review of this book was written by Allan Rossman. ("The American Statistician", May 1995 49(2) p. 237.)
And here is your next president.
The Economist, Dec 23, 1995, pp 31-33
This article begins by reminding us of four superstitious claims purporting to determine
the party that will win the presidential election. A chart gives the records for
these claims for elections since 1948. The results are: the Democrat will win if
hemlines are up early in election year (8 out of 11); its a good year for Bordeaux (8
out of 12); A National League team wins the world series (8 out of 12). The incumbent
will win if the Dow Jones monthly average is higher in October than in January (7
out of 12)
The author remarks that, while opinion polls are only meant to tell how voters feel
on the day of the poll, close to election day the polls do a pretty good job of predicting
the winner. In the last election, every major poll indicated a Clinton victory.
On the other hand, mathematical models based on economic conditions, past history
of the parties, etc. are supposed to predict the winner well in advance. Unfortunately,
two of the best known models predicted victory for George Bush in the last election.
However, these models are being tuned up and most of them predict a Clinton victory
in the next election.
A new way of predicting the outcome is the "Iowa Political Futures Market". This
is a computerized political futures market where investors trade, in real money,
in future contracts representing the candidates. Introduced in the 1988 election
it easily out-performed opinion polls as a guide to the eventual results in both the '88 and '92
election. For example, in 1992 Clinton won 43.3 percent of the vote, Bush 37.7 percent,
and Ross Perot 19 percent. The day before the vote, the closing price of a Clinton
share was 43.2, a Bush share 37.5 and a Perot share was 19.3.
The market works as follows: sellers set an asking price for a share of a specific
candidate and buyers offer a bid price. A computer sorts the transactions and manages
the investors' accounts. After the election, shares are paid off at the rate of
$1 multiplied by the candidate's share of the vote. This vote-share market has not opened
up yet for 1996, but for more than a year investors have been trading contracts that
will be worth $1 if the candidate wins and nothing if he loses.
The current price of a share for Clinton or for his Republican opponent are both about
43. You can buy a share on the Republican who will be nominated. The price for
Dole is about 50 and for Gram about 10. You can learn more about the market and
become a trader by going to the Iowa Political Futures homepage
(1) What is the probability that one of the signs would achieve the success it did
since 1948 just by chance?
(2) Why do you think the Iowa Political Futures does so well at prediction the outcome
of an election?
The next article was provided by Ann Watkins.
Study links leukemia in infants to alcohol; Mom's drinking increases risk.
Star Tribune, 3 Jan. 1996, p 1A
Babies born to women who drink alcohol during the last six months of pregnancy are
10 times more likely to develop leukemia during infancy, Minnesota researchers reported
in the "Journal of the National Cancer Institute". Infant leukemia is extremely
rare, even with the steep increase associated with drinking mothers. But researcher Xiao-Ou
Shu of the University of Minnesota said the study emphasizes that pregnancy and alcohol
should not be mixed.
The alcohol study is based on interviews with the parents of children who developed
leukemia by the age of 18 months. For comparison, the researchers also interviewed
the parents of 558 healthy children. Shu said that only about 32 babies per million
live births develop leukemia before 18 months in the United States. Shu said her research
showed that the rate increases to about 32 babies per 100,000 live births among drinking
How could the researchers come up with the 32 babies per 100,000 from this study?
What assumptions are being made in this estimate?
Could you conclude from this study that drinking during pregnancy promotes the development
of leukemia in infants? If not, why not?
Allan Rossman writes:
The following is an excerpt from Michael Crichton's "The Lost
World" (Alfred A. Knopf 1995), his sequel to "Jurassic Park". I think it displays
some serious misunderstandings of probability.
Gambler's Ruin was a notorious and much-debated
statistical phenomenon that had major consequences
both for evolution, and for everyday life. "Let's
say you're a gambler," he said. "And you're playing
a coin-toss game. Every time the coin comes up heads
you win a dollar. Every time it comes up tails, you
lose a dollar."
"What happens over time?"
Harding shrugged. "The chances of getting either
heads or tails is even. So maybe you win, maybe you
lose. But in the end, you'll come out at zero."
"Unfortunately, you don't," Malcolm said. "If you
gamble long enough, you'll always lose- the gambler
is always ruined. That's why casinos stay in
business. But the question is, what happens over
time? What happens in the period before the gambler
is finally ruined?"
"Okay," she said. "What happens?"
If you chart the gambler's fortunes over time, what
you find is the gambler wins for a period, or loses
for a period. In other words, everything in the world
goes in streaks. It's a real phenomenon, and you see
it everywhere: in weather, in river flooding, in
baseball, in heart rhythms, in stock markets. Once
things go bad, they tend to stay bad. Like the old
folk saying that bad things come in threes. Complexity
theory tells us the folk wisdom is right. Bad things
cluster. Things go to hell together. That's the real
(1) What do you think of Harding's initial reaction that "in the end, you'll come
out at zero"?
(2) Is Malcolm correct in his argument about "why casinos stay in business"?
(3) Modify Malcolm's argument to explain why casinos do stay in business.
(4) How much truth is there to Malcolm's claim that "everything in the world goes
in streaks"? Can you think of other examples that illustrate or refute this?
(5) Perform some simulations to investigate Malcolm's theory.
(6) Track down some information about the real "Gambler's Ruin" problem.
(7) (Added by editor) We were once at a gambling conference and there was a discussion
about how casinos make their money. A casino owner stated: "Even if we were to
take the zeros off the roulette wheels, the players would still come in and play
until they lost their money and we would continue to make all kinds of money". How long
do you think such a casino would stay in business?
New Recipe for the GDP Leaves Sour Taste.
The Wall Street Journal, 21 Dec. 1995
The Commerce Department is devising a new method to calculate the gross domestic product
(GDP). The GDP is designed to measure the total of consumer spending, business investment,
government purchases and foreign trade for the United States.
Under the old system, the Commerce Department used prices of a recent "base" year,
1987, to value output in each part of the economy. Each product is then weighted
according to its price in the base year. The problem lies in the fact that relative
prices change. Economists say that this leads to distortions of the GDP. For instance,
the overstated contribution of computers to the GDP resulted from falling computer
prices and assigning them a weight according to 1987 figures. This overstatement
then led to a distorted GDP figure.
The government will now use a combination of preceding-year and current prices for
a range of products and services. One result is that the GDP reported as an index
whose individual components -- consumption, investment, government purchases and
net exports -- will no longer add to the total GDP.
The new system corrects the problem about assigning weights according to base years,
but it still doesn't address problems that artificially reduce GDP figures. For
instance, it doesn't capture the output of people in service jobs (high-tech services
like banking, medical care) that produce greater quality instead of a tangible product.
The GDP, according to many economists, understated both productivity and growth
even before the switch to the new calculation method.
Under the new method, growth will shrink by a half percentage point a year or more.
Productivity was rising in the 1990s at 2.2% a year (double the rate of the 1970s
and 1980s). Under the new math, the 1990s figure will only be 1.4%, about the same
as that for the 1970s and 1980s.
There have also been complaints that the GDP does not count unpaid work and that many
of the social and environmental costs it does count actually have a negative effect
on the people's welfare. The change does not address these complaints though others
are trying to design an index that does.
John White suggested that, in light of the current discussion of the budget deficit,
it is interesting to graph the federal debt as a percentage of the gross domestic
product. The relevant data for this can be found.
The current percentage is about 71% and, while it is rising, it is still quite a bit
smaller than in the mid 40's when it reached 127%.
On math.sci George Preston posed the following problem:
My wife and I go to a busy shop. We separate and
say we will meet up later. Now I know my wife
will be looking for me. Is there a greater probability
of our meeting within a given time if I stay in one
place and wait for her to come by or is it greater if
I also wander about or are they the same? My instinct
(as opposed to logic) is to stay in one place.
The following reply was received:
Let's say that the size of the store is N. If you
are both moving around randomly, the probability that
you will meet at a given time is 1/N, so the expected
time for meeting is N. If you stay put and she moves >
around the store, she doesn't need to look for you
twice in the same place, so the expected time for meeting
is N/2. If you both stay put, you will never find each
Therefore, you need to agree which one of you will move
around and look for the other. If you don't agree, the
optimal strategy is probably to move around.
Speaking from experience, the optimal strategy is to say
"Meet you at such-and-such a place at time when-and-when."
If, when you meet, one or more of you would like to continue
shopping, repeat the process.
Wei-Hwa Huang, email@example.com,
(1) Do you agree with Huang's solution?
(2) Without any prior agreement, does it make any difference
whether you stay fixed or wander around?
(3) Does the shape and layout of the store affect your choice of
strategy? What about you and your wife's browsing habits?
Note: There are obviously many variations that could be given for this problem. We
will give a prize for the most interesting variation we receive by the time of the
next Chance News.
Parade Magazine, 17 Dec. 1995, p. 8
Marilyn vos Savant
Marilyn is asked the following question.
Say 10 tickets are numbered 1 through 10 in a
drawing. Half the numbers are even and half are
odd. The first ticket is drawn, and it's No. 3
which is odd. That leaves five even number and four
odd ones. Doesn't this mean that the next ticket
to be drawn is more likely to be even? If I buy a
ticket at this point, wouldn't I have a better chance
of winning the next draw by choosing an even number?
Joe Ball, Pittstown, NJ
Marilyn replies with the following rather cryptic answers.
Yes and no. Yes, the next number to be drawn is more
likely to be even, but no, you would not increase your
chances by choosing an even number. That is, if you
could place a bet that the next number would be even,
you'd win more often than you'd lose; after all, there
are more even numbers left.
But that's not an option. Instead, you must choose a
particular even number. Say, it's No. 2. Because
there aren't any more 2's than any other number, your
chances of winning are only 1 in 9--the same as if you'd
chosen any one of those other numbers--including the
(1) What is the correct answer to Joe's question?
(2) What is Marilyn trying to say?
Note: A reader (alas, name misplaced) sent us a letter to the editor of the Albany
newspaper "Times Union" commenting on Marilyn's answer in her Nov. 26 column to
the following question:
How much room would each person have if the Earth's
total population were uniformly spread over the land
area of planet Earth?
Marilyn said "546 square feet" (the area of a large living room) when she should have
said "a square whose side was 546 feet" (6.6 acres). The letter writer comments
that, for Marilyn to be correct, the population of the earth would have to be 3 trillion
rather that the present population of 5.6 billion.
Star Tribune, 28 Dec. 1995
Harper's magazine publishes each month the Harper's index, a page of statistics chosen
to surprise, amuse, and inform. Every member of the staff is asked to be on the
lookout in everything they read for potential index items. Interns research the
top contenders for legitimacy. This article provides the index from the January issue of
Harpers along with the sources. Here are some that amused us from their list of
Number of articles published since 1990 that mention
the danger of standing between Phil Gramm and a camera:
19 (Harper's research).
Number of U.S. sports arenas renamed for corporations
last year: 9 (Team Marketing Report: Chicago).
Percentage of Americans who favor placing ads on the
dollar bill to help cut the deficit or lower taxes : 35
(Visa/Plus ATM Network : San Francisco)
Estimated percentage of all U.S. television cartoon
programs that are drawn in Asia : 90 (Hanna-Barbera
Average indoor temperature, in degrees Fahrenheit:
23 (Borton Oversees: Minneapolis, Minn).
(1) How many of these statements do you believe?
(2) What is 23% Celsius in Farenheit?
'95 is hottest year on record as the global trend resumes.
The New York Times, 4 Jan. 1996
William K. Stevens
Preliminary figures from two sources indicate that the average surface temperature
reached a record high last year. British data gave the average temperature last
year as 58.72 degrees Fahrenheit. The previous record since records started being
kept in 1856 was 58.65 in 1995. The other estimate was 59.7 from data kept by the NASA Goddard
Institute for Space Studies in New York.
This record, along with the fact that the last five years average is higher than any
previous five-year period, is considered additional evidence of global warming.
Recent findings of the United Nations panel of scientists attributed the global warming
effect partially to human activity, in particular to the emission of heat-trapping
gases such as carbon dioxide, released by burning coal, petroleum products and wood.
A graph tracks the world temperature from 1856 to the present.
Hello 75, so long 55.
US News & World Report, 18 December 1995, pp71-75.
This is a long piece on the repeal of the national speed limit, a story reported in
the last edition of CHANCE news. It contains a number of tables and graphics that
would make good discussion items. On p 72 a pair of times series plots entitled
"Mixed Message" is presented. The first shows that the number of annual deaths on the interstates
has hovered around 4500 for the last 21 years (the only really large dip appearing
in 1974). The second shows that the rate of deaths--expressed as fatalities per
100 million miles traveled--has fallen nearly linearly from 2.3 to 0.9 (the one really
sharp drop again being in 1974). A caption attributes the decline to "more cars
and more miles traveled."
Another data table, entitled "Interstate Numbers", lists the 10 deadliest states (again
measured by fatalities per 100 million miles traveled). Large states with sparse
populations (1. Alaska, 2.077; 2. Nevada, 1.757; 3. Montana, 1.603) lead the list;
congestion and bad weather are cited as factors that reduce speed--and therefore fatalities--in
the safest states (1. Massachusetts, 0.337; Minnesota, 0.363; Michigan , 0.387).
(1) In what sense is the message "mixed" in the first graphic described? How can
the observed trends be accounted for?
(2) In what ways is "death rate per 100 million miles traveled" a good way to compare
states for highway travel safety? In what ways could it be misleading?
Recombinations: From Konigsberg to modern times; ECONOMIC PRINCIPLES.
The Boston Globe, 31 December, 1995, p 55
A wide-ranging essay, touching on topics from conbinatorics and the Konigsberg bridge
problem to Eric Lander's research at the Whitehead Institute on mapping the human
genome. An intriguing passage describes the use of mathematics and statistics to
"squeeze the most possible information out of various observations of lower organisms...[using]...simple
DNA spelling differences as markers on chromosomal strands...Now any family's history
could be viewed as a natural experiment..." Unfortunately few further details are presented on these ideas.
Please send comments and suggestions for articles to
CHANCE News 5.01
(11 Dec. 1995 to 8 Jan. 1996)