| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from large data set |
| Difficulty | Easy -1.8 This is a straightforward AS-level statistics question requiring only direct application of standard formulas for mean (Σx/n) and standard deviation (√(Σx²/n - x̄²)). Part (b) asks for basic interpretation about sampling and recall of dataset information. All calculations are routine with no problem-solving or conceptual challenge beyond formula recall. |
| Spec | 2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| 16(a)(i) | Obtains correct mean | |
| AWFW [0.053, 0.054] | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 16(a)(ii) | Obtains a value of the standard |
| Answer | Marks | Guidance |
|---|---|---|
| [0.0265, 0.0285] | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT 0.0275 | 1.1b | B1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 16(b)(i) | States that the claim is/may be |
| Answer | Marks | Guidance |
|---|---|---|
| database | 2.2b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 16(b)(ii) | States CO , CO or NOX | |
| 2 | 1.2 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Question 16 Total | 5 | |
| Q | Marking instructions | AO |
Question 16:
--- 16(a)(i) ---
16(a)(i) | Obtains correct mean
AWFW [0.053, 0.054] | 1.1b | B1 | 1 2 8 .6 5 7
Mean = = 0.053496
2 4 0 5
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 16(a)(ii) ---
16(a)(ii) | Obtains a value of the standard
deviation in the range
[0.0265, 0.0285] | 1.1b | B1 | 2
8.701707 128.657
Sd = −
2405 2405
= 0 . 0 0 0 7 5 6 3 9
= 0.0275
Obtains value of the standard
deviation
AWRT 0.0275 | 1.1b | B1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 16(b)(i) ---
16(b)(i) | States that the claim is/may be
incorrect.
With a valid reason
Eg
Not every make of car is
included in the LDS
LDS does not reflect number of
electric, gas/petrol in UK
database
Not every region is included in
the LDS
LDS only comes from 2 years
LDS is a small sample
compared to the entire UK
database | 2.2b | E1 | The LDS does not include cars
from every region of the UK, so the
claim may be incorrect.
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 16(b)(ii) ---
16(b)(ii) | States CO , CO or NOX
2 | 1.2 | B1 | CO
2
Subtotal | 1
Question 16 Total | 5
Q | Marking instructions | AO | Marks | Typical solutionAn investigation into the hydrocarbon emissions, $X$ g/km, from cars in the Large Data Set was carried out.
The results are summarised below.
$$\sum x = 128.657 \qquad \sum x^2 = 8.701 \, 707 \qquad n = 2405$$
where $n$ is the total number of cars which had a measured hydrocarbon emission in the Large Data Set.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the mean of $X$
[1 mark]
\item Find the standard deviation of $X$
[2 marks]
\end{enumerate}
\item \begin{enumerate}[label=(\roman*)]
\item The Large Data Set is a sample taken from the entire UK Department for Transport Stock Vehicle Database.
It is claimed that the values in part (a)(i) and part (a)(ii) obtained from the Large Data Set should be reliable estimates for the mean and standard deviation of the hydrocarbon emissions for the entire UK Department for Transport Stock Vehicle Database.
State, with a reason, whether this claim is likely to be correct.
[1 mark]
\item State one type of emission where more than 80% of the data is known for cars in the entire UK Department for Transport Stock Vehicle Database.
[1 mark]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2024 Q16 [5]}}