Donald Burrill wrote:
>If the data are normally distributed (or even approximately so, what
>seems to be called "empirically distributed" these days), the 3rd
>quartile + 1.5 IQR locates a point 2.0 std. devs. above the mean;
>symmetrically, the 1st quartile minus 1.5 IQR gets you 2.0 SDs below the
>mean. Close enough to the central 95% of the distribution, for the
>precision of the "1.5".
>
>Of course, the antique "5% standard" is rather out of fashion nowadays,
>but this was, I believe, the underlying rationale for Tukey's choice of
>the region "box +/- 1.5 IQR" as a rule-of-thumb (or convention) for
>initial identificaiton of potential outliers.
>
>On the question of whether the "whiskers" of a box-&-whisker plot should
>be made to cease at "box +/- 1.5 IQR", note that some current
>undergraduate textbooks distinguish between a "quick boxplot" which
>shows the range but not outliers, and a "full boxplot" which uses the
>"box +/- 1.5 IQR" rule. (Of course, if there are no outliers -- by that
>definition -- the two are identical.)
Interesting. As noted in earlier posts, the National Council of Mathematics
Teachers and MCAS include only the quick boxplot in their definition of
boxplot. The 10th grade MCAS test question 39 shows a quick boxplot, not a
Tukey boxplot. I can imagine that it would be difficult to change the NCMT
definition of boxplot, but I would hope that they should put a note in their
definition that their boxplot differs from the Tukey boxplot. Massachusetts'
Dept of Ed mentions the concept of standard deviation for the first time in the
11th - 12th grade math curriculum guidelines, so it can't be included in the
curriculum- based and high-stakes 10th grade math test.
Since 45% of MA 10th graders failed the last year's 10th grade test, this
morning's headlines in Boston's papers reveal that the Gov of MA will announce
today that she will make up to $1000 available to any student that fails the
test three times. The $1000 can be used for private tutors, textbooks or
software. A student has 5 chances to pass the exam which is required for
graduation:
http://www.boston.com/dailyglobe2/242/metro/Swift_seeks_grants_to_MCAS_str
ugglers+.shtml
Unfortunately, there is only a bit over a month between the late October
failure notices on last spring's Math test and the first of 4 retakes in
December. I would imagine only students right on the cusp would stand much of
a chance of improving their knowledge of content for this first retake. They
certainly could learn how to interpret a quick boxplot or a stem-and-leaf
diagram (asked on last year's test), but not anything more substantive.
One would hope that the MCAS testers review their statistics and
probabilityquestions. Here is a problematic probability question from this
spring's 8th grade math test. Because of the inappropriate premise, part c is
either very difficult to answer (two different answers 1/3 or 1/8) or
unanswerable if students are allowed to be in the same act.
8th grade math, 2001 MCAS test, Question 12:
12. An eight grade class will perform the first four acts in the annual talent
show. Every student is in exactly one of the four acts. The order in which
the acts will be presented is to be decided by drawing so that each act has an
equal chance of being drawn.
a. Chantal is a member of the eighth grade class. What is the probability that
her act will be presented first?
b. Chantal's act was chosen to be presented first. Make a tree diagram, chart
or list showing all the possible orders in which the other three acts could be
presented. Use the letters A, B, and C to represent these three acts.
c. Rory, Jesse, and Chantal are all members of the eighth-grade class who will
each perform an act. What is the probability that Rory's act will immediately
follow Jesse's? Explain how you found your answer.
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