**Be Wary
of H.S. Statistics **

By **Jerome Dancis**, Associate Professor
Emeritus, Math Dept., Univ. of MD

Reading and
Arithmetic-level data analysis (Statistics) is very important for all.
This
means knowledge and understanding of averages, medians, percentiles,
box and
whisker diagrams; also being able to read and draw a variety of graphs,
charts
and tables[1]
as well as proficiency with percents and decimals and the *big*
bugaboo, word problems.
This is more important than Algebra. The
rush to Algebra, should be replaced by the careful
development of student proficiency in reading Arithmetic word problems
and
Arithmetic-level data analysis.

Unfortunately many
high school and some college graduates are *not*
well versed in Arithmetic data analysis.
As a U.S. Dept. of Education study[2]
noted: "É far fewer [Americans] are leaving higher education with the
skills needed to comprehend routine data, such as reading a table about
the
relationship between blood pressure and physical activity, É 'What's
disturbing
is that the assessment is ...
[designed] to test your ability to read labels,' [Mark S. Schneider,
commissioner of education statistics] added." [3]

The Common Core Math curriculum (which
is about to become the next national [not federal] math curriculum)
does ** not**
include students knowing percentiles or knowing that a 50% off sale
means half
price or even that 50% = 1/2.

The Common CoreÕs GlossaryÕs definition[4]
of Òfirst quartileÓ is WRONG!

A prerequisite for
understanding random variables in Statistics, is understanding (the far
simpler) variables (the xÕs) in Algebra.
Proficiency in translating word problems into Algebraic formulas
is the
basis for writing formulas for spreadsheets.

CollegesÕ attitude
to freshmen, with **zero** K-12
Statistics, is: *No Statistics;
no problem*. Colleges are
reasonably successful at teaching Statistics Ð
at *least*
to those students, who are fluent in Arithmetic and Algebra. Many are *not *[5].

The choice, of which statistical method
to use
usually depends on context, context, context, that is, *on how the
information will be used*. For example, on my
campus, psychology majors are required to take PSYC 200, ÒStatistical
Methods
in PsychologyÓ, which builds on PSYC 100, ÒIntroduction to PsychologyÓ.
Business majors are required to take BMGT 230, ÒBusiness StatisticsÓ. Sociology majors take SOCY 201,
ÒIntroduction Statistics for SociologyÓ, which builds on SOCY 100. This spring, we taught 41 classes of
these three specialized beginning courses in Statistics.
In addition the Mathematics Dept.
taught 8 classes
of STAT 100. ÒElementary Statistics and
ProbabilityÓ.

An eleventh grader,
doing well in Algebra II, has several math options for Grade 12,
including Pre-Calculus
and AP Statistics. Learning Pre-Calculus
will make him/her fully ready for all college majors, including STEM
majors. But, taking AP Statistics will
likely
put him/her at-risk for college majors in statistics and engineering.

Common Core Math Standards prescribed a
Statistics strand for high and middle school. Also,
a weak Algebra II syllabus. Time on
Statistics will take time away from Algebra.
This may increase the numbers of students needing to retake high school
Algebra
II in college.

That college math
professors consider
statistics
and probability to be *optional *courses
in high school is reflected in their statement that statistics and
probability
are two of Òseveral
mathematics courses that could be
considered reasonable for study once students have achieved a strong
background
in algebra and geometryÓ [6].

That students are *not*
obtaining competency with Arithmetic-level data analysis is
indicated by the following Problem
1, which stymied more than 5 of 8 (65%) Grade 9
students, when it was field tested in Maryland (MD).

**Problem 1.**[7] "The table below
shows how a typical household spends money on utilities.

__Utility Percentage of Total Utility
Costs__

Lighting 6

Refrigeration 9

Water heating 14

Appliances 27

Heating and cooling 44.

A typical household spent $1,400 on
utilities last
year. If there are no significant changes in their utility usage for
this year,
how much should they budget for heating and cooling their home this
year?

[Multiple Choice] F $196 G
$378 H $616 J $784 "

**Comment**. Students had *calculators*
to
calculate 44% of $1400 or they
might simply notice that H $616 is the only choice that is a
little
less than $1400/2.

**Data
analysis is often too tricky for high
school. ** It
is

**MD
Assessment Item on ****Data Analysis**** **** [8]**. ÒIn a
small town, 250 randomly sampled
registered voters were asked to state whether they would vote ÒYesÓ or
ÒNoÓ on
Measure A in the next local election. The table below shows the results
of the
survey.

**VOTER SURVEY RESULTS**

**Yes**
**No**
**Undecided**

96
34
120

There are 5,500 people expected to vote
in the
next election. Based on the data, how many people will vote ÒNoÓ on
Measure A
in the next election?Ó

Students who answered
2,112, were
marked *correct* on the 2007 MD state
assessment. To obtain this answer of
2,112, students are expected to make a number of unwarranted and
usually
*incorrect* assumptions [9]. But, students who answer 2,112,
on a college political science
exam will likely be marked *wrong*; a
correct answer would be: *not* enough
information is provided for the list of reasons noted in the footnote. [10]

Again, Data analysis is often *too
tricky* for high school: UMCP
Physics
Professor, Tom Cohen's, observations of his child (a student in
Montgomery
County Public Schools, MD) doing her
Algebra/ data analysis homework on "best fit" lines:

"However, the
way data analysis is taught and tested troubles me. ...
[11] The issues are subtle and algebra one
students are not prepared to deal with them. Thus, the students are
being
miseducated in data analysis and statistics.Ó

ÒIn my view this
treatment is worse than useless, it is positively destructive. Students
are
told in essence to plug things in which they don't understand and then
to trust
the answers. This is diametrically opposed to the critical reasoning
about data
analysis that we need to instill in students.Ó

[1]
Professor
of Biological Sciences, at Towson State University, MD, Virginia
Anderson,
Ed.D., reported needing to provide extensive training to her college
biology
students in the reading and drawing of tables, graphs and charts.

[2] Conducted by the National Center for Education Statistics.

[3] "Literacy
of College Graduates Is on Decline
Survey's Finding of a Drop in Reading Proficiency Is
Inexplicable,
Experts Say", Washington Post, December 25, 2005; A12

[4] ÒFirst
quartile. For a data set with median M, the
first quartile is the median of the data values less than M. ! This
leads to the first quartile for the data set {1,
3, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7} being 3. WRONG, it is 7.

[5]
From a Univ. of
MD, College Park [UMCP]
instructor: ...
[on] a recent quiz I gave in STAT
100 [our college version of AP Stat] ... .
Most
all [students] obtained the [correct] equation y = .52 + .7x, but many
(over
half of my class) missed points because they did not correctly graph
the
line. ... the line they drew ...
was not y = .52 + .7x, but some arbitrary line. ...,
a [student] commented, "Well, I graphed it on my
calculator, shouldn't I get credit for that?" When
I mentioned that I needed the scale, y-intercept,
slope, etc. correctly graphed ... , the reply was, ".... the calculator
doesn't show the scale so I don't know how to do that."

Another question on the quiz ...
given
that the equation ... y = -36.9 + 5.07x, [find y when x = 20]. I had more than one student who forgot his/her
calculator
say they couldn't do this problem because they didn't have a calculator
(i.e.
couldn't do decimal multiplication and addition).

FYI
... the text assumes
students know [how to graph a line] before taking STAT 100..

[6]
This was noted in the Ò[College
ProfessorsÕ Concerns on]
Mathematical Preparedness of Incoming College FreshmenÓ, the only
statement on
college preparedness issued by The MD/DC/VA Section of the Mathematical
Association of America (MAA). On
the web at: http://sections.maa.org/mddcva/HS_students.php

[7] Sample MD High School
Assessment on Algebra and Data Analysis, Item 48 [2000]

[8]
This is 2007 Public
Release Algebra/Data
Analysis Item #38 at

http://mdk12.org/assessments/high_school/look_like/2007/algebra/ftri38.html

This is also Item
#37 at

http://www.mdk12.org/assessments/high_school/look_like/2007/algebra/hsaAlgebra.pdf

[9] The number of people,
who will
actually vote in the next election, is exactly (not just approximately)
equal
to the number expected to vote.

None of the undecided
people will make up their mind and choose to vote ÒNoÓ after the survey. This is rarely a true statement.

All of the surveyed
people, who answered, ÒundecidedÓ were actually undecided.
Nobody said ÒundecidedÓ as a polite way
to say ÒNone of your businessÓ.

[10] Incorrect assumptions listed in preceding footnote.

[11] ÒIn particular, the use of linear regressions (done by a calculator) to fit lines is not appropriate for algebra one students, in my view. The students are NOT taught what a "best fit" line means mathematically, how to judge whether the model fits the data well ... nor even given any clear way to understand whether the data ought to fit a line. If you ask the calculator for a line which will fit points which lie on a parabola the calculator will spit back a [misleading] line and the students will dutifully write it down.Ó