| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Histogram from discrete rounded data |
| Difficulty | Moderate -0.8 This is a routine grouped data statistics question requiring standard formula application (mean, standard deviation from grouped data), basic histogram frequency density calculation, and conceptual understanding of median location and effect of data changes. All techniques are textbook exercises with no problem-solving or novel insight required, making it easier than average but not trivial due to the multi-part nature and need for careful calculation. |
| 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 |
| \(l\) | 10-12 | 13-15 | 16-20 | 21-30 |
| Frequency | 1 | 13 | 20 | 6 |
40 people were asked to guess the length of a certain road. Each person gave their guess, $l$ km, correct to the nearest kilometre. The results are summarised below.
\begin{tabular}{|l|c|c|c|c|}
\hline
$l$ & 10-12 & 13-15 & 16-20 & 21-30 \\
\hline
Frequency & 1 & 13 & 20 & 6 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item \begin{enumerate}[label=(\alph*)]
\item Use appropriate formulae to calculate estimates of the mean and standard deviation of $l$. [6]
\item Explain why your answers are only estimates. [1]
\end{enumerate}
\item A histogram is to be drawn to illustrate the data. Calculate the frequency density of the block for the 16-20 class. [2]
\item Explain which class contains the median value of $l$. [2]
\item Later, the person whose guess was between 10 km and 12 km changed his guess to between 13 km and 15 km. Without calculation state whether the following will increase, decrease or remain the same:
\begin{enumerate}[label=(\alph*)]
\item the mean of $l$, [1]
\item the standard deviation of $l$. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2010 Q2 [13]}}