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Box&Whisker Plots/ Five Number Summary
Posted:
Oct 2, 1996 8:30 PM


In reviewing several texts, I find that some use the Q1 & Q3 points in the five number summary, while others use the upper/lower hinge points. A cursory check makes it appear that these points are probably identical except when n mod 4 =3 with n the number of data points. The TI82 uses the Q1 & Q3 points in its Box & Whisker plot, I would guess this is a TI standard approach. Finally some computer programs use a linear approximation to the quartiles.
One point of interest is whether students will be required to use a specific method on the exam. A second point is whether they would be expected to use the quick box plot, or the full box plot with identification and marking of outliers.
To this point, despite the fact that my text uses hinge points, I have chosen to use the quartiles for the box plot and have recommended to my students that the quick box plot is a quickanddirty approach with appropriate consideration given to whether the plot suggests further examination via the full plot.
Finally, I have spent two (45 minute periods)days in having the students calculating variance using only the lists available on the TI82 so that they will understand how it is calculated and in particular the terminology applied to Mean Squared Deviation. Once I am confident they understand the methodology, and terminology they will be using the TI82 values directly. I should remark that the first third of this course is NOT being considered AP level at our school. The idea was to attract as many good (not necessarily great) students as possible to provide an introduction to at least part of the field with the hope that many would remain for the AP portion.
In any case, I have three questions concerning the exam: (1) Will the 5 number summary use quartiles? (2) If a Box & Whisker is requested, can we safely assume it is intended to be the quick box? (3) Is it likely that a student will be requested to find a variance without access to the calculator?
Thanks for any information.



