| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | December |
| Marks | 6 |
| Topic | Measures of Location and Spread |
| Type | Clean or interpret large data set structure |
| Difficulty | Moderate -0.8 This question tests basic understanding of mean calculations and proportions with straightforward arithmetic. Part (a) requires simple conceptual understanding of how omitting data affects means, (b) involves routine mean calculation with given values, and (c)-(d) require basic proportion calculations and interpretation. All steps are standard procedures with no problem-solving insight required. |
| Spec | 2.02f Measures of average and spread |
| Data extract for one LA in 2001 | |||
| Work mainly at or from home | UMLT | Train | Bus, minibus or coach |
| 295 | – | 4 | 4 |
| Year | 2001 | 2011 |
| Total number of employees | 23 627 753 | 26 526 336 |
Using the 2001 UK census results and some software, Javid intended to calculate the mean number of people who travelled to work by underground, metro, light rail or tram (UMLT) for all 348 Local Authorities. However, Javid noticed that for one LA the entry in the UMLT column is a dash, rather than a 0. See the extract below.
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{4}{|c|}{Data extract for one LA in 2001} \\
\hline
Work mainly at or from home & UMLT & Train & Bus, minibus or coach \\
\hline
295 & – & 4 & 4 \\
\hline
\end{tabular}
\end{center}
Javid felt that it was not clear how this LA was to be treated so he decided to omit it from his calculation.
\begin{enumerate}[label=(\alph*)]
\item Explain how the omission of this LA affects Javid's calculation of the mean. [1]
\end{enumerate}
The value of the mean that Javid obtained was 2046.3.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the value of the mean when this LA is not removed. [2]
\end{enumerate}
Javid finds that the corresponding mean for all Local Authorities for 2011 is 2860.8. In order to compare the means for the two years, Javid also finds the total number of employees in each of these years. His results are given below.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Year & 2001 & 2011 \\
\hline
Total number of employees & 23 627 753 & 26 526 336 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that a higher proportion of employees used the metro to travel to work in 2011 than in 2001. [2]
\item Suggest a reason for this increase. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2018 Q10 [6]}}