© 2008 The Author Teaching Statistics. Volume 30, Number 3, Autumn 2008 • 65Journal compilation © 2008 Teaching Statistics Trust

Editorial 65

CURRICULUM MATTERSImplementing New Reform Guidelines in TeachingIntroductory College Statistics Courses 66Michelle Everson, Andrew Zieffler and Joan Garfield

People Graphs in Primary School 71Diane Sales

Degrees of Freedom 75Joseph G. Eisenhauer

An Exponential Misconception 79Holly Zullo

Teaching Statistical Concepts, Fundamentals andModelling 81Timothy E. O’Brien

The Unrelenting Exchange Paradox 86Ruma Falk

Illustrating Dependence between Random VariablesUsing Slot Machines 89Ian N. Durbach and Graham D. I. Barr

STATISTICAL DIVERSIONS 93Peter Petocz and Eric Sowey

CONTENTS

� News and Notes 96 � Index to Volume IBC

TEACHING STATISTICS

Turning to the current issue of Teaching Statistics, youwill find comments tangential to the above discussion inthe article on statistical concepts by O’Brien. Discus-sion of the American Statistical Association’s GAISEguidelines and their implementation may be found inthe article by Everson, Zieffler, and Garfield. Salesexplores the use of “people” graphs. Eisenhauer helpsus come to grips with the notion of degrees of freedom.Zullo discusses difficulties encountered by studentswhen they try to simulate a queuing system. For aninteresting paradox and its resolution, see the article byFalk. Slot machines are used by Durbach and Barr todiscuss statistical dependence. Finally, Petocz and Soweydiscuss both physical laws and statistical laws in theirStatistical Diversions column.

For further details on the recursive procedure given onthe cover, by the way, see the 1962 Technometrics articleby Welford entitled “Note on a method for calculatingcorrected sums of squares and products” (vol. 4, no. 3,pp. 419–420).

Roger JohnsonEditor

The formulae on the cover of this issue provide a wayto recursively compute the sample mean and samplevariance. In particular, given the sample mean x(n) andsample variance s2(n) for the data x1, x2, . . . , xn theseformulae indicate how the sample mean and samplevariance are updated when an additional data point xn+1

is observed. Why would you use such formulae? In short,they produce accurate results when implemented on acomputer. Using a computer to determine the samplevariance using what is sometimes called the “short-cut”method, on the other hand, will tend to give veryinaccurate results when the values in the data set arelarge and very nearly equal. As a statistician workingfor the U.S. Navy I encountered data for which therecursive formulae gave accurate results but for whichthe “short-cut” method gave a negative sample variance!

At any rate, the cover is primarily meant to be a bit of atease for an article by Daved Muttart that will appearin the next issue of Teaching Statistics. While the recur-sive procedure on the cover appears in few, if any,elementary statistics texts, elementary texts often do givealternatives to the definitional formulae. You will findthat Daved has a very clear view on the role of suchcomputational formulae within the curriculum!

E D I T O R I A L