\documentclass[12pt]{article}\usepackage{ammaths}\en
\begin{document}
\module{The consultant task}{1}{06}{1 period}
\prereq{}
\object{\begin{itemize}
\item Use statistics to make a decision.
\end{itemize}}
\mater{\begin{itemize}
\item Slideshow.
\item Info sheets in enveloppes with selected infos about the situation.
\end{itemize}}
For this activity, the class is divided in groups of (ideally) 6 pupils.
\modpart{The cast}{5 mins}
The pupils in each group of 6 have to act as administrators of a large school :
\begin{itemize}
\item 1 headmaster ;
\item 1 deputy headmaster ;
\item 1 school accountant ;
\item 1 teacher ;
\item 1 representative of the regional council ;
\item 1 representative of the parents.
\end{itemize}
\modpart{The situation}{10 mins}
The teacher explains the situation with a slideshow, emphasizing the decision that has to be made.
\begin{quote}
To improve students' test scores on state assessments, administrators from a large school require students to take
practice exams. Two outside consultants create and score the open-ended questions from these exams. Although both
consultants use the same general scheme to score student responses, the administrators suspect that the two consultants
do not interpret and apply the scheme in the same way, resulting in differences in scores between the exams scored by
the two consultants. The consultants' contracts with the school are up for renewal, and the administrators are trying
to decide if they should be renewed. They decide to use the most recent practice exam to compare the scores assigned
from each consultant and to decide whether there is a difference in the way the exams are scored. The administrators
select 50 exams scored by the first consultant and 50 exams scored by the second consultant. They find that the average
score for the 50 exams scored by the first consultant is 9.7 (out of a possible 15 points), while the average score for
the 50 exams scored by the second consultant is 10.3 (out of a possible 15 points). What should the administrators
conclude about the scores assigned by these two consultants ?
\end{quote}
\pagebreak
\modpart{The discussion}{Remaining time}
Each group of students have to discuss the situation together.
When they need additionnal information, they ask the teacher who's playing the parts of the two consultants. He sends
the additional info as a letter in an enveloppe. If a group doesn't ask for information the teacher can nevertheless
send a letter to help the discussion move forwards.
The comity has to come to a decision at the end of the hour.
Additionnal information are, in the order they should be handed out :
\begin{itemize}
\item the standard deviations of the two sets of exams (with a mistake) ;
\item the dot plots for the two sets of exams (with a mistake) ;
\item the standard deviations and dot plots of the two sets of exams (corrected) ;
\item the raw data - this one should only be given at the end.
\end{itemize}
\pagebreak
\moddocdis{The consultant task}{1}{06}{Info sheet \#1}
\begin{center}
{\large\bf\textsf{Standard deviations}}
\end{center}
While the \emph{mean} is a statistical measure of central tendency, the \emph{standard deviation} is a measure of
dispersion. Even though the computation itself is a bit complicated, intuitively it gives an idea of how the values are
spread. It shows how much variation there is from the mean. A low standard deviation indicates that the data points tend
to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large range
of values. With scores out of a possible 15 points, a standard deviation close to 1 would be considered very small,
while a standard deviation equal to 5 or more would be very high.
\begin{center}
\begin{tabular}{|l|c|c|}
\hline
& \bf Consultant 1 & \bf Consultant 2 \\
\hline
\bf First quartile & 7 & 6 \\
\hline
\bf Median & 11 & 7.5 \\
\hline
\bf Third quartile & 12 & 8 \\
\hline
\bf Mean & 9.7 & 10.3 \\
\hline
\bf Standard deviation & 3.376 & 20.205 \\
\hline
\end{tabular}
\end{center}
\pagebreak
\moddocdis{The consultant task}{1}{06}{Info sheet \#2}
\begin{center}
{\large\bf\textsf{Dot plots}}
\end{center}
\begin{center}
{\bf Consultant 1}\par
\medskip
\psset{xunit=0.8cm,yunit=0.25cm}
\begin{pspicture}(-1,-1)(16,14)
\psaxes(0,0)(16,0)
\psdots(2,1)(3,1)(3,2)(4,1)(4,2)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)(7,1)(7,2)(7,3)(8,1)(8,2)(8,3)(8,4)(8,5)(9,1)(10,1)
(10,2)(10,3)(11,1)(11,2)(11,3)(11,4)(11,5)(11,6)(11,7)(11,8)(12,1)(12,2)(12,3)(12,4)(12,5)(12,6)(12,7)(12,8)(12,9)
(13,1)(13,2)(13,3)(13,4)(14,1)(14,2)(14,3)(14,4)(14,5)(15,1)
\end{pspicture}
\end{center}
\bigskip
\begin{center}
{\bf Consultant 2}\par
\medskip
\psset{xunit=0.8cm,yunit=0.25cm}
\begin{pspicture}(-1,-1)(16,14)
\psaxes(0,0)(16,0)
\psdots(5,1)(5,2)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)(6,7)(6,8)
(6,9)(6,10)(6,11)(6,12)(6,13)(7,1)(7,2)(7,3)(7,4)(7,5)
(7,6)(7,7)(7,8)(7,9)(7,10)(8,1)(8,2)(8,3)(8,4)(8,5)
(8,6)(8,7)(8,8)(8,9)(8,10)(8,11)(8,12)(8,13)(9,1)(9,2)
(9,3)(9,4)(9,5)(9,6)(9,7)(9,8)(10,1)(10,2)(11,1)
\end{pspicture}
\end{center}
\pagebreak
\moddocdis{The consultant task}{01}{06}{Info sheet \#3}
\begin{center}
{\large\bf\textsf{Corrected standard deviations and dot plots}}
\end{center}
\begin{center}
\begin{tabular}{|l|c|c|}
\hline
& \bf Consultant 1 & \bf Consultant 2 \\
\hline
\bf First quartile & 7 & 6 \\
\hline
\bf Median & 11 & 7.5\\
\hline
\bf Third quartile & 12 & 8 \\
\hline
\bf Mean & 9.7 & 7.6 \\
\hline
\bf Standard deviation & 3.376 & 1.726 \\
\hline
\end{tabular}
\end{center}
\bigskip
\begin{center}
{\bf Consultant 1}\par
\medskip
\psset{xunit=0.8cm,yunit=0.25cm}
\begin{pspicture}(-1,-1)(16,14)
\psaxes(0,0)(16,0)
\psdots(2,1)(3,1)(3,2)(4,1)(4,2)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)(7,1)(7,2)(7,3)(8,1)(8,2)(8,3)(8,4)(8,5)(9,1)(10,1)
(10,2)(10,3)(11,1)(11,2)(11,3)(11,4)(11,5)(11,6)(11,7)(11,8)(12,1)(12,2)(12,3)(12,4)(12,5)(12,6)(12,7)(12,8)(12,9)
(13,1)(13,2)(13,3)(13,4)(14,1)(14,2)(14,3)(14,4)(14,5)(15,1)
\end{pspicture}
\end{center}
\bigskip
\begin{center}
{\bf Consultant 2}\par
\medskip
\psset{xunit=0.8cm,yunit=0.25cm}
\begin{pspicture}(-1,-1)(16,14)
\psaxes(0,0)(16,0)
\psdots(5,1)(5,2)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)(6,7)(6,8)
(6,9)(6,10)(6,11)(6,12)(6,13)(7,1)(7,2)(7,3)(7,4)(7,5)
(7,6)(7,7)(7,8)(7,9)(7,10)(8,1)(8,2)(8,3)(8,4)(8,5)
(8,6)(8,7)(8,8)(8,9)(8,10)(8,11)(8,12)(8,13)(9,1)(9,2)
(9,3)(9,4)(9,5)(9,6)(9,7)(9,8)(10,1)(10,2)(11,1)(15,1)
\end{pspicture}
\end{center}
\pagebreak
\moddocdis{The consultant task}{01}{06}{Info sheet \#4}
\begin{center}
{\large\bf\textsf{Raw data}}
\end{center}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{\bf Consultant 1} & \multicolumn{2}{|c|}{\bf Consultant 1} \\
\hline
Score & Frequency & Score & Frequency \\
\hline
0 & 0 & 0 & 0 \\
\hline
1 & 0 & 1 & 0 \\
\hline
2 & 1 & 2 & 0 \\
\hline
3 & 2 & 3 & 0 \\
\hline
4 & 2 & 4 & 0 \\
\hline
5 & 0 & 5 & 2 \\
\hline
6 & 6 & 6 & 13 \\
\hline
7 & 3 & 7 & 10 \\
\hline
8 & 5 & 8 & 13 \\
\hline
9 & 1 & 9 & 8 \\
\hline
10 & 3 & 10 & 2 \\
\hline
11 & 8 & 11 & 1 \\
\hline
12 & 9 & 12 & 0 \\
\hline
13 & 4 & 13 & 0 \\
\hline
14 & 5 & 14 & 0 \\
\hline
15 & 1 & 15 & 1 \\
\hline
\end{tabular}
\end{center}
\end{document}