| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Compare using calculated statistics |
| Difficulty | Moderate -0.8 This is a straightforward AS-level statistics question requiring basic calculations (mean and standard deviation from given data) and interpretation. Part (a) is routine calculator work, part (b)(i) is simple percentage calculation, and part (b)(ii) tests knowledge of sampling limitations—all standard textbook material with no novel problem-solving required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| \multirow{2}{*}{2002} | 0.031 | 0.019 | 0.091 | 0.025 | 0.030 | 0.061 |
| 0.047 | 0.029 | 0.059 | 0.363 | 0.330 | 0.376 |
| \multirow{2}{*}{2016} | 0.005 | 0.047 | 0.053 | 0.063 | 0.026 | 0.013 |
| 0.058 | 0.012 | 0.010 | 0.010 | 0.008 | 0.008 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Mean \(= 0.026\) | B1 | AO1.1b – States mean \(= 0.026\); AWRT |
| Standard deviation \(= 0.021\) | B1 | AO1.1b – States correct standard deviation; AWRT 0.021 or 0.022 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\% \text{ drop} = \frac{0.122 - 0.026}{0.122} \times 100 = 78.7\%\) | M1 | AO1.1a – Finds 'their' % drop; or calculates 'their' mean as a % of 0.122; or calculates 25% or 75% of \(0.122\) |
| \(78.7\% > 75\%\) | A1F | AO2.2b – Compares 'their' 79% to 75; or compares 'their' 21% to 25; or shows 'their' mean \(< 0.0305\) or \((0.122 -\) 'their' mean\() > 0.0915\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The LDS only includes a limited number of makes of car so cannot make a claim about all makes of cars | E1 | AO2.4 – Makes one appropriate comment on the validity of the claim |
| The LDS does not include cars from all areas of the UK so cannot make a claim about cars from all areas of the UK | E1 | AO2.4 – Makes a second different comment; also accept: too small a sample; limited NOX emission data in LDS |
## Question 13(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Mean $= 0.026$ | B1 | AO1.1b – States mean $= 0.026$; AWRT |
| Standard deviation $= 0.021$ | B1 | AO1.1b – States correct standard deviation; AWRT 0.021 or 0.022 |
---
## Question 13(b)(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\% \text{ drop} = \frac{0.122 - 0.026}{0.122} \times 100 = 78.7\%$ | M1 | AO1.1a – Finds 'their' % drop; or calculates 'their' mean as a % of 0.122; or calculates 25% or 75% of $0.122$ |
| $78.7\% > 75\%$ | A1F | AO2.2b – Compares 'their' 79% to 75; or compares 'their' 21% to 25; or shows 'their' mean $< 0.0305$ or $(0.122 -$ 'their' mean$) > 0.0915$ |
---
## Question 13(b)(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| The LDS only includes a limited number of makes of car so cannot make a claim about all makes of cars | E1 | AO2.4 – Makes one appropriate comment on the validity of the claim |
| The LDS does not include cars from all areas of the UK so cannot make a claim about cars from all areas of the UK | E1 | AO2.4 – Makes a second different comment; also accept: too small a sample; limited NOX emission data in LDS |13 Two random samples of 12 NOX emissions (in $\mathrm { g } / \mathrm { km }$ ) were taken from the Large Data Set.
One sample was taken from the 2002 data and the other sample from the 2016 data.\\
The sample data are shown below:
\begin{center}
\begin{tabular}{ | l | l l l l l l | }
\hline
\multirow{2}{*}{2002} & 0.031 & 0.019 & 0.091 & 0.025 & 0.030 & 0.061 \\
& 0.047 & 0.029 & 0.059 & 0.363 & 0.330 & 0.376 \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | l l l l l l | }
\hline
\multirow{2}{*}{2016} & 0.005 & 0.047 & 0.053 & 0.063 & 0.026 & 0.013 \\
& 0.058 & 0.012 & 0.010 & 0.010 & 0.008 & 0.008 \\
\hline
\end{tabular}
\end{center}
The mean and standard deviation of the 2002 sample data are 0.122 and 0.137 respectively.
13
\begin{enumerate}[label=(\alph*)]
\item Find the mean and standard deviation of the 2016 sample data giving your answers correct to three decimal places.\\
13
\item Siti claims these samples show that, on average, the NOX emissions across all makes of car in all areas of the UK have fallen by over 75\% between 2002 and 2016.
13 (b) (i) Show how Siti's claim of 'over 75\%' has been obtained.\\
13 (b) (ii) Using your knowledge of the Large Data Set, make two comments on the validity of Siti's claim.
Comment 1\\
\section*{Comment 2}
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2022 Q13 [6]}}