| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Identify outliers using mean and standard deviation |
| Difficulty | Moderate -0.8 This is a straightforward S1 statistics question requiring basic calculations (mean, standard deviation) and application of the standard outlier rule (typically Q1 - 1.5×IQR or mean ± 2 standard deviations). All parts are routine textbook exercises with no conceptual challenges or novel problem-solving required, making it easier than average for A-level. |
| Spec | 2.02g Calculate mean and standard deviation2.02h Recognize outliers |
A sprinter runs many 100-metre trials, and the time, $x$ seconds, for each is recorded. A sample of eight of these times is taken, as follows.
10.53 \quad 10.61 \quad 10.04 \quad 10.49 \quad 10.63 \quad 10.55 \quad 10.47 \quad 10.63
\begin{enumerate}[label=(\roman*)]
\item Calculate the sample mean, $\bar{x}$, and sample standard deviation, $s$, of these times. [3]
\item Show that the time of 10.04 seconds may be regarded as an outlier. [2]
\item Discuss briefly whether or not the time of 10.04 seconds should be discarded. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q4 [7]}}