| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Moderate -0.8 This is a routine S1 statistics question requiring standard calculations from a frequency table (median, quartiles, mean, standard deviation) and basic interpretation. The calculations are straightforward applications of formulas, and part (b)(ii) tests understanding that the 95% rule applies to normal distributions, not all distributions. While multi-part with several marks, it requires no problem-solving insight beyond textbook methods. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| \multirow{2}{*}{Number of goals scored in a match} | Number of matches | |
| 2004/05 | 2005/06 | |
| 0 | 30 | 32 |
| 1 | 79 | 82 |
| 2 | 99 | 95 |
| 3 | 68 | 78 |
| 4 | 60 | 48 |
| 5 | 24 | 30 |
| 6 | 11 | 9 |
| 7 | 6 | 6 |
| 8 | 2 | 0 |
| 9 | 1 | 0 |
| Total | 380 | 380 |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | 11 | 9 |
Question 6:
6 | 11 | 96 For each of the Premiership football seasons 2004/05 and 2005/06, a count is made of the number of goals scored in each of the 380 matches. The results are shown in the table.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
\multirow{2}{*}{Number of goals scored in a match} & \multicolumn{2}{|r|}{Number of matches} \\
\hline
& 2004/05 & 2005/06 \\
\hline
0 & 30 & 32 \\
\hline
1 & 79 & 82 \\
\hline
2 & 99 & 95 \\
\hline
3 & 68 & 78 \\
\hline
4 & 60 & 48 \\
\hline
5 & 24 & 30 \\
\hline
6 & 11 & 9 \\
\hline
7 & 6 & 6 \\
\hline
8 & 2 & 0 \\
\hline
9 & 1 & 0 \\
\hline
Total & 380 & 380 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item For the number of goals scored in a match during the 2004/05 season:
\begin{enumerate}[label=(\roman*)]
\item determine the median and the interquartile range;
\item calculate the mean and the standard deviation.
\end{enumerate}\item Two statistics students, Jole and Katie, independently analyse the data on the number of goals scored in a match during the 2005/06 season.
\begin{itemize}
\item Jole determines correctly that the median is 2 and that the interquartile range is also 2.
\item Katie calculates correctly, to two decimal places, that the mean is 2.48 and that the standard deviation is 1.59 .
\begin{enumerate}[label=(\roman*)]
\item Use your answers from part (a), together with Jole's and Katie's results, to compare briefly the two seasons with regard to the average and the spread of the number of goals scored in a match.
\item Jole claims that Katie's results must be wrong as $95 \%$ of values always lie within 2 standard deviations of the mean and $( 2.48 - 2 \times 1.59 ) < 0$ which is nonsense.
\end{itemize}
Explain why Jole's claim is incorrect. (You are not expected to confirm Katie's results.)
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q6 [12]}}