| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate mean from coded sums |
| Difficulty | Easy -1.2 This is a straightforward application of coding transformations for mean and standard deviation. Part (a) requires basic calculation of mean and SD from given data, then applying the simple rules that adding a constant affects the mean but not the SD. Part (b) involves scaling by a constant, which affects both statistics proportionally. All steps are routine recall of standard formulas with no problem-solving or conceptual challenges beyond remembering the transformation rules. |
| Spec | 2.02g Calculate mean and standard deviation |
2 Before leaving for a tour of the UK during the summer of 2008, Eduardo was told that the UK price of a 1.5-litre bottle of spring water was about 50p.
Whilst on his tour, Eduardo noted the prices, $x$ pence, which he paid for 1.5-litre bottles of spring water from 12 retail outlets.
He then subtracted 50 p from each price and his resulting differences, in pence, were
$$\begin{array} { l l l l l l l l l l l l }
- 18 & - 11 & 1 & 15 & 7 & - 1 & 17 & - 16 & 18 & - 3 & 0 & 9
\end{array}$$
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the mean and the standard deviation of these differences.
\item Hence calculate the mean and the standard deviation of the prices, $x$ pence, paid by Eduardo.
\end{enumerate}\item Based on an exchange rate of $€ 1.22$ to $\pounds 1$, calculate, in euros, the mean and the standard deviation of the prices paid by Eduardo.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-05_2484_1709_223_153}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2010 Q2 [7]}}