| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Session | Specimen |
| Marks | 6 |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring basic calculations from a frequency table (mean and standard deviation using standard formulas) and qualitative discussion about outliers. Part (i) is routine A-level statistics; parts (ii) and (iii) require only conceptual understanding rather than complex reasoning. Easier than average A-level content. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| \(x\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| frequency | 3 | 10 | 4 | 3 | 2 | 0 | 0 | 0 | 1 |
**(i)** $(\Sigma f = 23$, $\Sigma xf = 43$, $\Sigma x^2f = 149)$
State mean $= 1.87$ B1
Attempt standard deviation formula $= \sqrt{\frac{\Sigma x^2 f}{n-1} - \bar{x}^2}$ *OR* $\sqrt{\frac{\Sigma x^2 f}{n} - \bar{x}^2}$
and obtain 1.81 or 1.73 or better B1 **[2]**
**(ii)(a)** The outlier would be removed as a difference of 8 is impossible B1 **[1]**
**(b)** The outlier would be included if it is a valid data entry B1 **[1]**
**(iii)** The mean would be reduced (1.59) B1
Standard deviation would be reduced (1.23 or 1.15) B1 **[2]**12 A set of data is shown in the table below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | }
\hline
$x$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
frequency & 3 & 10 & 4 & 3 & 2 & 0 & 0 & 0 & 1 \\
\hline
\end{tabular}
\end{center}
(i) Calculate the mean and standard deviation of the data.
The value 8 may be regarded as an outlier.\\
(ii) Explain how you would treat this outlier if the data represents
\begin{enumerate}[label=(\alph*)]
\item the difference of the scores obtained when throwing a pair of ordinary dice,
\item the number of thunderstorms per year in Cambridgeshire over a 23-year period.\\
(iii) Without doing any further calculations state what effect, if any, removing the outlier would have on the mean and standard deviation.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 Q12 [6]}}