| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| 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 straightforward S1 statistics question requiring basic skills: identifying the mode from a frequency table, finding median/quartiles by counting positions, recognizing that mean and range need exact values from open-ended classes, then calculating them with given data. All techniques are standard textbook exercises with no problem-solving or novel insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| Number of visitors | Number of days |
| 20 or fewer | 1 |
| 21 | 2 |
| 22 | 3 |
| 23 | 6 |
| 24 | 8 |
| 25 | 10 |
| 26 | 13 |
| 27 | 7 |
| 28 | 2 |
| 29 | 1 |
| 30 or more | 2 |
| Total | 55 |
2 A small chapel was open to visitors for 55 days during the summer of 2015. The table summarises the daily numbers of visitors.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Number of visitors & Number of days \\
\hline
20 or fewer & 1 \\
\hline
21 & 2 \\
\hline
22 & 3 \\
\hline
23 & 6 \\
\hline
24 & 8 \\
\hline
25 & 10 \\
\hline
26 & 13 \\
\hline
27 & 7 \\
\hline
28 & 2 \\
\hline
29 & 1 \\
\hline
30 or more & 2 \\
\hline
Total & 55 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item For these data:
\begin{enumerate}[label=(\roman*)]
\item state the modal value;
\item find values for the median and the interquartile range.
\end{enumerate}\item Name one measure of average and one measure of spread that cannot be calculated exactly from the data in the table.\\[0pt]
[2 marks]
\item Reference to the raw data revealed that the 3 unknown exact values in the table were 13,37 and 58.
Making use of this additional information, together with the data in the table, calculate the value of each of the two measures that you named in part (b).\\[0pt]
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2016 Q2 [8]}}