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\Large
\noindent{\bf Ma 12 Long Test 1\hfill 9 February 2017}
\medskip\hrule
\begin{enumerate}
\item The weights in kilos of a group of individuals are as follows:
\begin{center}
$%
\begin{array}{ccccccc}
46 & 51 & 52 & 53.5 & 56 & 60 & 61.6 \\
66 & 69.4 & 70 & 70 & 72 & 73 & 75 %
\end{array}%
$
\end{center}
\begin{enumerate}
\item How many classes should be used for the frequency distribution?
\item What should be the class width?
\item Construct the frequency distribution for the data set
\item Construct a histogram for the data set
\end{enumerate}
\item Given the following data set:
\begin{center}
$%
\begin{array}{cccccccccc}
2 & 12 & 13 & 14 & 16 & 16 & 17 & 19 & 20 & 20 \\
23 & 24 & 24 & 24 & 27 & 40 & 42 & 60 & 70 & 79 %
\end{array}%
$
\end{center}
\begin{enumerate}
\item Determine the quartiles
\item Construct a box plot for the data set
\item Is the data skewed to the left or to the right?
\end{enumerate}
\item The following represents the average life span of smokers according to the average number of cigars they smoke in a day:
\begin{center}
$%
\begin{array}{ccccc}
\text{No. of cigars} & 5 & 10 & 15 & 20
\\
\text{Life span} & 65 & 56 & 48 & 40 %
\end{array}%
$
\end{center}
Let $x$ represent the number of cigars and $y$ the life span.
\begin{enumerate}
\item Find the least squares line for the data set (use two decimal places).\hfill[20]
\item Use this model to predict the average life span of a person who smokes 25 cigars daily (round-off to the nearest year).\hfill[5]
\end{enumerate}
\item The following data gives the number of bacteria in a culture (in billions):
\begin{center}
$%
\begin{array}{ccccc}
\text{Time (in minutes)} & 0 & 1 & 2 & 3 \\
\text{Population} & 7.4 & 8.2 & 30.1 & 50.8%
\end{array}%
$
\end{center}
Let $x$ be the number of minutes and $y$ the bacteria population:
\begin{enumerate}
\item Construct a scatter plot for the data set.\hfill[12]
\item Does the data follow a linear trend?
\item Linearize the data set
\item Find the least squares line for the linearized data set \hfill[8]
\item Predict the bacteria population after 10 minutes.\hfill[5]
Note: Answers should be correct to four decimal places for this item.
\end{enumerate}
\begin{center}
$m=\dfrac{n\sum xy -\sum x\sum y}{n\sum x^2 -(\sum x)^2}$
$b=\dfrac{\sum x^2\sum y - \sum x\sum xy}{n\sum x^2 -(\sum x)^2}$
\end{center}
\end{enumerate}
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