| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Paper | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then find median/quartiles from cumulative frequency |
| Difficulty | Moderate -0.3 This is a standard S1 statistics question covering routine histogram construction, interpolation for median, and basic summary statistics calculations. While multi-part with several marks, each component follows textbook procedures with no novel problem-solving required, making it slightly easier than average A-level difficulty. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Delay (mins) | Number of motorists |
| \(4 - 6\) | 15 |
| \(7 - 8\) | 28 |
| 9 | 49 |
| 10 | 53 |
| \(11 - 12\) | 30 |
| \(13 - 15\) | 15 |
| \(16 - 20\) | 10 |
5. The following grouped frequency distribution summarises the number of minutes, to the nearest minute, that a random sample of 200 motorists were delayed by roadworks on a stretch of motorway.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Delay (mins) & Number of motorists \\
\hline
$4 - 6$ & 15 \\
\hline
$7 - 8$ & 28 \\
\hline
9 & 49 \\
\hline
10 & 53 \\
\hline
$11 - 12$ & 30 \\
\hline
$13 - 15$ & 15 \\
\hline
$16 - 20$ & 10 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Using graph paper represent these data by a histogram.
\item Give a reason to justify the use of a histogram to represent these data.
\item Use interpolation to estimate the median of this distribution.
\item Calculate an estimate of the mean and an estimate of the standard deviation of these data.
One coefficient of skewness is given by
$$\frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } } .$$
\item Evaluate this coefficient for the above data.
\item Explain why the normal distribution may not be suitable to model the number of minutes that motorists are delayed by these roadworks.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5}}