| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 8 |
| Topic | Measures of Location and Spread |
| Type | Removing data values |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring basic skills: identifying skewness from a frequency distribution, applying the standard outlier rule (1.5×IQR), and correcting a mean calculation. All parts use routine A-level statistics techniques with no conceptual challenges or novel problem-solving required. |
| Spec | 2.02f Measures of average and spread2.02h Recognize outliers |
| Birth weight (w kg) | \(2.0 \leqslant w < 2.5\) | \(2.5 \leqslant w < 3.0\) | \(3.0 \leqslant w < 3.5\) | \(3.5 \leqslant w < 4.0\) | \(4.0 \leqslant w < 4.5\) |
| Frequency | 1 | 6 | 9 | 17 | 10 |
The table summarises 43 birth weights as recorded for babies born in a particular hospital during one week.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Birth weight (w kg) & $2.0 \leqslant w < 2.5$ & $2.5 \leqslant w < 3.0$ & $3.0 \leqslant w < 3.5$ & $3.5 \leqslant w < 4.0$ & $4.0 \leqslant w < 4.5$ \\
\hline
Frequency & 1 & 6 & 9 & 17 & 10 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item State the type of skewness of the data. [1]
\item Given that the lower quartile is 3.21 kg and the upper quartile is 3.96 kg, determine whether there are any babies whose birth weights might be regarded as outliers. [4]
\item The mean birth weight was found to be 3.58 kg. However, it was discovered subsequently that the table includes the birth weight, 2.52 kg, of one baby that has been recorded twice. Find the mean birth weight after this error has been removed. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q5 [8]}}