| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| Marks | 10 |
| Paper | 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 standard calculations from a frequency table: identifying the modal class, finding median/IQR by cumulative frequency, and computing mean/standard deviation using midpoints. All techniques are routine textbook exercises with no problem-solving insight required, making it easier than average A-level maths questions. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Daily number of letters (x) | Number of days (f) |
| 0-9 | 5 |
| 10-19 | 16 |
| 20 | 23 |
| 21 | 27 |
| 22 | 31 |
| 23 | 34 |
| 24 | 16 |
| 25-29 | 10 |
| 30-34 | 5 |
| 35-39 | 3 |
| 40-49 | 4 |
| 50 or more | 1 |
| Total | 175 |
2 Katy works as a clerical assistant for a small company. Each morning, she collects the company's post from a secure box in the nearby Royal Mail sorting office.
Katy's supervisor asks her to keep a daily record of the number of letters that she collects.
Her records for a period of 175 days are summarised in the table.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Daily number of letters (x) & Number of days (f) \\
\hline
0-9 & 5 \\
\hline
10-19 & 16 \\
\hline
20 & 23 \\
\hline
21 & 27 \\
\hline
22 & 31 \\
\hline
23 & 34 \\
\hline
24 & 16 \\
\hline
25-29 & 10 \\
\hline
30-34 & 5 \\
\hline
35-39 & 3 \\
\hline
40-49 & 4 \\
\hline
50 or more & 1 \\
\hline
Total & 175 \\
\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 The most letters that Katy collected on any of the 175 days was 54. Calculate estimates of the mean and the standard deviation of the daily number of letters collected by Katy.
\item During the same period, a total of 280 letters was also delivered to the company by private courier firms.
Calculate an estimate of the mean daily number of all letters received by the company during the 175 days.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2012 Q2 [10]}}