| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from raw data list |
| Difficulty | Easy -1.3 This is a straightforward S1 statistics question requiring standard procedures: identifying the mode by inspection, finding median/quartiles using cumulative frequency positions (n+1)/2 etc., calculating range, and estimating mean/SD from grouped data using midpoints. All techniques are routine recall with minimal problem-solving, though the grouped data adds minor computational work. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| Number of matches | Number of boxes |
| Less than 239 | 1 |
| 239-243 | 1 |
| 244-246 | 2 |
| 247 | 3 |
| 248 | 4 |
| 249 | 6 |
| 250 | 10 |
| 251 | 13 |
| 252 | 16 |
| 253 | 20 |
| 254 | 5 |
| 255-259 | 3 |
| More than 259 | 1 |
| Total | 85 |
1 The number of matches in each of a sample of 85 boxes is summarised in the table.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Number of matches & Number of boxes \\
\hline
Less than 239 & 1 \\
\hline
239-243 & 1 \\
\hline
244-246 & 2 \\
\hline
247 & 3 \\
\hline
248 & 4 \\
\hline
249 & 6 \\
\hline
250 & 10 \\
\hline
251 & 13 \\
\hline
252 & 16 \\
\hline
253 & 20 \\
\hline
254 & 5 \\
\hline
255-259 & 3 \\
\hline
More than 259 & 1 \\
\hline
Total & 85 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item For these data:
\begin{enumerate}[label=(\roman*)]
\item state the modal value;
\item determine values for the median and the interquartile range.
\end{enumerate}\item Given that, on investigation, the 2 extreme values in the above table are 227 and 271 :
\begin{enumerate}[label=(\roman*)]
\item calculate the range;
\item calculate estimates of the mean and the standard deviation.
\end{enumerate}\item For the numbers of matches in the 85 boxes, suggest, with a reason, the most appropriate measure of spread.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2011 Q1 [11]}}