Living HistogramsAuthor(s): Brian L. JoinerSource: International Statistical Review / Revue Internationale de Statistique, Vol. 43, No. 3(Dec., 1975), pp. 339-340Published by: International Statistical Institute (ISI)Stable URL: http://www.jstor.org/stable/1403117Accessed: 02/12/2009 06:58

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Int. Stat. Rev., Vol. 43, No. 3, 1975, pp. 339-340/Longman Group Ltd/Printed in Great Britain

Living Histograms

Brian L. Joiner Statistics Department, The University of Wisconsin - Madison

Summary Most students and indeed society as a whole tend to think of statistics as a dull subject having to do with endless columns of numbers, and having little to do with people or other interesting things. Thus it becomes very useful to have teaching aids that help to demonstrate to students that statistics is a "live" interesting subject which finds application throughout the real world.

The pictures in Figures 1 through 4 were taken to help make statistics come more alive to students who are not numerically nor algebraically oriented. These pictures can be used to demonstrate a number of important statistical concepts, including: statistical distributions, histograms, the normal "bell-shaped" curve, scatter plots, correlation, mean, median, mode, range, hetrogeneous populations and unsuspected correlations. Some further details are given in the captions.

The students in the pictures are from two introductory statistics classes and one introductory psychology class. We asked for volunteers in these three classes and virtually all of the students volunteered. We checked the heights and weights of the few who declined to participate and found no significant differences. In fact, all of the non-participants seemed to have quite legitimate reasons for being elsewhere at the scheduled time. Thus it does not appear that these figures are biased to any significant extent due to non-response.

The basic idea for these pictures stems from Youden's Experimentation and Measurement (1962) which has a picture similar to Figure 1 based on the heights of potted plants. Subse- quently, sketches similar to Figures 1 and 3 were discovered in references [Kafka (1950)] and

[Silverman, Eliot and Brody (1973)]. Eight by ten inch glossy prints of Figures 1 to 4 and several other pictures are available from

the author for $2.00 each to cover costs. Other pictures available include the corresponding pictures for males and pictures showing "Eleven 50 per cent non-parametric, extreme order statistic, confidence intervals based on n = 2" and "Seven 87-5 per cent non-parametric, extreme order statistic, confidence intervals based on n = 4". Standard two by two inch 35 mm colour slides are also available for $1.00 each.

The assistance of many students and colleagues is gratefully acknowledged, as is the intrepid courage of photographer James F. Lukens.

References

Kafka, F. (1950). Statistics Without Numbers. Lifetime Editions, Inc., New York. Silverman, Eliot N.; Brody, Linda A. (1973). Statistics: A Common Sense Approach. Prindle, Weber and

Schmidt, Inc., Boston, Mass. Youden, W. J. (1962). Experimentation and Measurement. Scholastic Book Services, New York.

1 This work was done while the author was at The Pennsylvania State University.

340

Resume

La plupart des etudiants, et en fait la societe dans son ensemble, ont tendance a consid6rer les statistiques comme un sujet ennuyeux, s'interessant a des colonnes sans fin de chiffres, mais de peu d'interet pour les individus, ou autres domaines dignes d'attention. C'est pourquoi il devient tr6s utile de pouvoir disposer d'auxiliaires d'enseignement, aidant a montrer aux 6tudiants que les statistiques constituent un sujet int6ressant et "vivant", qui trouve des applications dans tout l'univers reel. Les dessins des figures 1 a 4 ont ete choisis dans le but d'aider a faire des statistiques quelque chose de plus vivant aux yeux des 6tudiants dont l'orientation n'est pas tournee vers les domaines du nombre et de l'algebre. Ces dessins peuvent etre utilis6s pour presenter beaucoup de concepts statistiques importants, notamment: distributions statistiques, histogrammes, courbe normale "en cloche", dispersion, correlation, moyenne, m6diane, mode, 6tendue, populations h6terogenes, et correlations non douteuses.

Figure i. tistogram oj a sample oj college jemales arrangea oy nelgnt. ror example, me two grins at tne leit are both 4 feet 11 inches, the next five are all 5 feet tall and so on. Notice the "bell-shaped" curve formed by the fact that many girls have the same height near the average, while fewer and fewer girls have any given height as one movesfarther from the average. (See article on page 339.)

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Figure 2. Histogram of a sample of college students arranged by height. Note that this histogram has a bi-modal shape due to the mixing of two separate groups, males and females.

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Figure 3. Scatter plot of college females arranged according to their height and weight. For example, the girl at the lower left is 4 feet 11 inches tall and weighs about 90 or 95 pounds. Note the correlation between height and weight depicted by this plot. The average weight of taller girls is appreciably more than the average weight of shorter ones.

Figure 4. Scatter plot of college females positioned according to their heights and grade point averages. Interestingly enough, there does appear to be some correlation between these two variables with taller girls tending to have higher grade point averages.