| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Standard combined mean and SD |
| Difficulty | Easy -1.2 This is a straightforward AS-level statistics question requiring only basic mean calculation (sum/n) and subtraction. Part (b) and (c) involve simple data interpretation rather than mathematical computation. No complex problem-solving or novel insight required—purely routine application of the mean formula. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| \cline { 2 - 3 } \multicolumn{1}{c|}{} | \(\mathbf { 2 0 0 2 }\) | \(\mathbf { 2 0 1 6 }\) |
| \(\sum \boldsymbol { x }\) | 207901 | 142103 |
| Sample size | 1215 | 1144 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\text{Mean}_{2002} = 171\), \(\text{Mean}_{2016} = 124\) | M1 (1.1a) | Obtains either 171 or 124 AWRT |
| Reduction \(= 171 - 124 = 47\) (or 27% reduction) | A1 (1.1b) | AWRT |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Disagree — there are very few cars of these types in the LDS in 2016, so they alone cannot have caused this reduction in mean emissions | E1 (2.4) | Must refer to small number (1 of each) of these car types in 2016 data |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1215 + 1144 = 2359 \neq 3827\), so total sample size is 2359, different from LDS size (3827), implying 1468 missing/extra | E1 (2.4) | Must show total sample size is 2359 and indicate this differs from 3827 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| The claim is incorrect because the LDS also has a 'Company' car category | E1 (2.4) | Must indicate LDS has other categories |
## Question 16(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\text{Mean}_{2002} = 171$, $\text{Mean}_{2016} = 124$ | M1 (1.1a) | Obtains either 171 or 124 AWRT |
| Reduction $= 171 - 124 = 47$ (or 27% reduction) | A1 (1.1b) | AWRT |
## Question 16(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Disagree — there are very few cars of these types in the LDS in 2016, so they alone cannot have caused this reduction in mean emissions | E1 (2.4) | Must refer to small number (1 of each) of these car types in 2016 data |
## Question 16(c)(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1215 + 1144 = 2359 \neq 3827$, so total sample size is 2359, different from LDS size (3827), implying 1468 missing/extra | E1 (2.4) | Must show total sample size is 2359 and indicate this differs from 3827 |
## Question 16(c)(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| The claim is incorrect because the LDS also has a 'Company' car category | E1 (2.4) | Must indicate LDS has other categories |16 An analysis was carried out using the Large Data Set to compare the $\mathrm { CO } _ { 2 }$ emissions (in g/km) from 2002 and 2016.
The summary statistics for the $\mathrm { CO } _ { 2 }$ emissions, $X$, for all cars registered as owned by either females or males is given in the table below.
\begin{center}
\begin{tabular}{ | c | c | c | }
\cline { 2 - 3 }
\multicolumn{1}{c|}{} & $\mathbf { 2 0 0 2 }$ & $\mathbf { 2 0 1 6 }$ \\
\hline
$\sum \boldsymbol { x }$ & 207901 & 142103 \\
\hline
Sample size & 1215 & 1144 \\
\hline
\end{tabular}
\end{center}
16
\begin{enumerate}[label=(\alph*)]
\item Find the reduction in the mean of the $\mathrm { CO } _ { 2 }$ emissions in 2016 compared to the mean of the CO2 emissions in 2002.\\
16
\item It is claimed that the move to more electric and gas/petrol powered cars has caused the reduction in the mean $\mathrm { CO } _ { 2 }$ emissions found in part (a).
Using your knowledge of the Large Data Set, state whether you agree with this claim.\\
Give a reason for your answer.\\
16
\item There are 3827 data values in the Large Data Set.
It is claimed that the data in the table above must have been summarised incorrectly.\\
16 (c) (i) Explain why this claim is being made.
16 (c) (ii) State whether this claim is correct.\\
Give a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2021 Q16 [5]}}