Moderate -0.8 This is a standard S1 statistics question testing routine procedures: identifying class boundaries, calculating histogram bar heights using frequency density, linear interpolation for quartiles, and describing skewness. All techniques are textbook exercises requiring careful arithmetic but no problem-solving insight or novel reasoning.
The table shows the time, to the nearest minute, spent waiting for a taxi by each of 80 people one Sunday afternoon.
Waiting time
(in minutes)
Frequency
\(2 - 4\)
15
\(5 - 6\)
9
7
6
8
24
\(9 - 10\)
14
\(11 - 15\)
12
Write down the upper class boundary for the \(2 - 4\) minute interval.
A histogram is drawn to represent these data. The height of the tallest bar is 6 cm .
Calculate the height of the second tallest bar.
Estimate the number of people with a waiting time between 3.5 minutes and 7 minutes.
Use linear interpolation to estimate the median, the lower quartile and the upper quartile of the waiting times.
Describe the skewness of these data, giving a reason for your answer.
\begin{enumerate}
\item The table shows the time, to the nearest minute, spent waiting for a taxi by each of 80 people one Sunday afternoon.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | }
\hline
\begin{tabular}{ c }
Waiting time \\
(in minutes) \\
\end{tabular} & Frequency \\
\hline
$2 - 4$ & 15 \\
\hline
$5 - 6$ & 9 \\
\hline
7 & 6 \\
\hline
8 & 24 \\
\hline
$9 - 10$ & 14 \\
\hline
$11 - 15$ & 12 \\
\hline
\end{tabular}
\end{center}
(a) Write down the upper class boundary for the $2 - 4$ minute interval.
A histogram is drawn to represent these data. The height of the tallest bar is 6 cm .\\
(b) Calculate the height of the second tallest bar.\\
(c) Estimate the number of people with a waiting time between 3.5 minutes and 7 minutes.\\
(d) Use linear interpolation to estimate the median, the lower quartile and the upper quartile of the waiting times.\\
(e) Describe the skewness of these data, giving a reason for your answer.\\
\hfill \mbox{\textit{Edexcel S1 2014 Q5 [12]}}