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\begin{document}

\noindent
{\Large 
Stats Worksheet IIf \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~202 \\
Spring Semester 2004}
\vspace{.25in}

\noindent
{\bf WARNING:}  You must {\bf SHOW ALL OF YOUR WORK}.  You will receive 
NO CREDIT if you do not show your work.

\noindent
{\bf DUE:} {\bf THURSDAY, 19 FEBRUARY 2004} 
\begin{enumerate} 
\item A Spanish 101 exam was given last Monday.  The scores for Section 006
are given below.
	\begin{center}
	\begin{tabular}{rrrrrr}
	23,& 78,& 90,& 100,& 56,& 87,\\
	67,& 37,& 100,& 77,& 83,& 89,\\
	92,& 90,& 45,& 30,& 2,& 78,\\
	87,& 98,& 67,& 95,& 94,& 13,\\
	21\\
	\end{tabular}
	\end{center}
    \begin{enumerate}
    \item Draw a line plot to represent these scores.
    \item Draw a stem and leaf plot to represent these scores.
    \item Draw a histogram to represent these scores.  
    You should label the horizontal axis with
    0--9, 10--19, 20--29, 30--39, 40--49, 50--59, 60--69,
    70--79, 80--89, and 90--100.
    \item What is the total area of all the columns in the histogram?  How
    does this relate to your data?
    \item Draw a line graph to represent these scores.
    You should label the horizontal axis with
    0--9, 10--19, 20--29, 30--39, 40--49, 50--59, 60--69,
    70--79, 80--89, and 90--100.
    \item Use your histogram to find the total area under the line graph
    and above the horizontal
    axis.  {\bf HINT:}{\em You will probably need to draw
    a large histogram on a full sheet of paper and use a pair of scissors.}
    \item Draw a bar graph to represent the grades on this exam. The grades
    are calculated as follows:
    	\begin{center}
	\begin{tabular}{|c|l|}
	\hline
	GRADE & SCORE \\
	\hline 
	\hline
	A & 90-100 \\
	B & 80-89 \\
	C & 70-79 \\
	D & 60-69 \\
	E & 0-59 \\
	\end{tabular}
	\end{center}
    \item Draw a pie chart to represent the grades on this exam.  Be sure
    to indicate the angles you used to construct the chart.
    \item Calculate the mean score.
    \item Calculate the median score.
    \item Find the mode.
    \item Find the upper quartile.
    \item Find the lower quartile.
    \item Find the Inner Quartile Range.
    \item Are there any outliers in this set of data?  If so, what are the
    outliers?
    \item Construct a Box and Whisker Plot for these scores.
    \item Find the Standard Deviation for these scores.
    \item What percent of the scores are within one standard deviation of
    the mean?
    \item What percent of the scores are within two standard deviations of
    the mean?
    \item What percent of the scores are within three standard deviation of
    the mean?
    \item Draw a relative frequency histogram for this data.  (That is to
    say, the vertical axis should denote the relative frequency of the
    scores, not the total number of students earning each score.) 
    You should label the horizontal axis with
    0--9, 10--19, 20--29, 30--39, 40--49, 50--59, 60--69,
    70--79, 80--89, and 90--100.
    \item What is the the total area of the columns in the relative
    frequency histogram.
    \item Draw a frequency polygon.
    \item What is the area of the shape under the frequency polygon and
    above the horizontal axis?
    \end{enumerate}
\item When analyzing a set of data, what two characteristics should be
measured.
\item When would you need to take a random sample?
\item What is the difference between a sample mean and a population mean?
between a sample standard deviation and a population standard deviation?
\item Can you think of a large set of data that does not have a normal
distribution?
\item {\bf TRUE or FALSE:}  Statistics are facts. 
\item Do number 15 on page 551.
\item Do number 16 on pages 550--551.
\item Do number 18 on page 551.
\item Do number 14 on page 572.
\item Do number 15 on page 572.
\item Do number 16 on page 572.
\item Do number 17 on page 572.
\item Do number 18 on page 572.
\item Do number 22 on page 573.
\item Do number 2 on page 584.
\item Do number 6 on page 584.
\item Do number 8 on page 585.
\item Do number 12 on page 585.
\noindent
%=============================================================================
\newpage
{\bf REVIEW}
\item Do number 9 on page 498 of your textbook.
\item 
	\be
	\item Write a function $A(r)$ for the area of a circle of radius
		$r$.
	\item Write a function $B(d)$ for the area of a circle of radius
		$d$.
	\item Find $A(2)$, $A(4)$, $A(3)$, $A(6)$, $A(.5)$, and $A(1)$.
		What do each of these values represent?  
	\item How does the area of a circle change when we double its
		radius?  Verify your answer using function notation. ({\em
		Hint:}  If we double the radius $r$, then the new radius
		is expressed by \spc.  Input the new radius into your area
		function $A$.)
	\item How does the area of a circle change when we double its
		diameter.  Verify your answer using function notation.
	\item Which is the better deal: three ten inch pizzas for $\$20$ or
		one twenty inch pizza for $\$20$?
	\item Write a function $P(r)$ for the perimeter of a circle with
		radius $r$.
	\item How does the perimeter of a circle change when we double its
		radius?  Verify your answer using function notation.
	\ee
\item Prove that $2\sqrt{3}-4$ is irrational.  You may use the fact that
$\sqrt{3}$ is irrational.
\item Jake can bake five dozen cookies in two hours.  Joni can bake eight
dozen cookies in two hours.  If they work together, how long will it take
them to bake twenty dozen cookies?
\end{enumerate}
\end{document}
