| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Identify outliers using mean and standard deviation |
| Difficulty | Moderate -0.8 This is a straightforward data handling question requiring basic statistical calculations (standard deviation from a calculator), identifying outliers using a given rule (2 SD from mean), and recognizing common data errors (zeros vs missing values). All parts are routine AS-level statistics with no problem-solving insight required—easier than average. |
| Spec | 2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Make | Region | Engine size | Mass | CO2 | CO |
| VAUXHALL | South West | 1398 | 1163 | 118 | 0.463 |
| VOLKSWAGEN | London | 999 | 1055 | 106 | 0.407 |
| VAUXHALL | South West | 1248 | 1225 | 85 | 0.141 |
| BMW | South West | 2979 | 1635 | 194 | 0.139 |
| TOYOTA | South West | 1995 | 1650 | 123 | 0.274 |
| BMW | South West | 2979 | 0 | 244 | 0.447 |
| FORD | South West | 1596 | 0 | 165 | 0.518 |
| TOYOTA | South West | 1299 | 1050 | 144 | |
| VAUXHALL | London | 1398 | 1361 | 140 | 0.695 |
| FORD | North West | 4951 | 1799 | 299 | 0.621 |
| Answer | Marks |
|---|---|
| 17(a)(i) | Correctly states the value of the |
| Answer | Marks | Guidance |
|---|---|---|
| standard deviation. | AO1.1b | B1 |
| Answer | Marks |
|---|---|
| 17(a)(ii) | Correctly explains that 4951 is an |
| Answer | Marks |
|---|---|
| outlier. | AO2.4 |
| Answer | Marks |
|---|---|
| AO2.1 | E1 |
| Answer | Marks |
|---|---|
| R1 | 2084.2 + 2×1161.95 = 4408 |
| Answer | Marks | Guidance |
|---|---|---|
| 17(b) | Infers that Rajan has incorrectly | |
| included the zero masses. | AO2.2b | E1 |
| Answer | Marks |
|---|---|
| 17(c) | Explains that not all values of the |
| Answer | Marks | Guidance |
|---|---|---|
| likely to be incorrect | AO2.2b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 17:
--- 17(a)(i) ---
17(a)(i) | Correctly states the value of the
standard deviation (AWRT 1162)
Accept AWRT 1225 using
unbiased estimate of population
standard deviation. | AO1.1b | B1 | Standard deviation = 1161.95
--- 17(a)(ii) ---
17(a)(ii) | Correctly explains that 4951 is an
outlier by comparing it with mean
+ 2sd
Correctly explains that 999 is not
an outlier by comparing it with
mean – 2sd
Completes a rigorous argument to
show that there is exactly one
outlier. | AO2.4
AO2.4
AO2.1 | E1
E1
R1 | 2084.2 + 2×1161.95 = 4408
4951 > 4408.15 so 4951 is an
outlier
2084.2 - 2×1161.95 = - 239.7
999 > -239.7 so 999 is not an
outlier
There is no other value greater
than 4408, therefore there is
only one outlier.
--- 17(b) ---
17(b) | Infers that Rajan has incorrectly
included the zero masses. | AO2.2b | E1 | Rajan has included the two
zeroes in the mass column, but
he should not have used them.
--- 17(c) ---
17(c) | Explains that not all values of the
CO emissions are known in the
LDS and infers Rajan’s claim is
likely to be incorrect | AO2.2b | E1 | The claim is likely to be incorrect
as not all values of CO
emissions are known in the
LDS.
Total | 6
Q | Marking Instructions | AO | Marks | Typical SolutionThe table below is an extract from the Large Data Set.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Make & Region & Engine size & Mass & CO2 & CO \\
\hline
VAUXHALL & South West & 1398 & 1163 & 118 & 0.463 \\
VOLKSWAGEN & London & 999 & 1055 & 106 & 0.407 \\
VAUXHALL & South West & 1248 & 1225 & 85 & 0.141 \\
BMW & South West & 2979 & 1635 & 194 & 0.139 \\
TOYOTA & South West & 1995 & 1650 & 123 & 0.274 \\
BMW & South West & 2979 & 0 & 244 & 0.447 \\
FORD & South West & 1596 & 0 & 165 & 0.518 \\
TOYOTA & South West & 1299 & 1050 & 144 & \\
VAUXHALL & London & 1398 & 1361 & 140 & 0.695 \\
FORD & North West & 4951 & 1799 & 299 & 0.621 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the standard deviation of the engine sizes in the table. [1 mark]
\item The mean of the engine sizes is 2084
Any value more than 2 standard deviations from the mean can be identified as an outlier.
Using this definition of an outlier, show that the sample of engine sizes has exactly one outlier.
Fully justify your answer. [3 marks]
\end{enumerate}
\item Rajan calculates the mean of the masses of the cars in this extract and states that it is 1094 kg.
Use your knowledge of the Large Data Set to suggest what error Rajan is likely to have made in his calculation. [1 mark]
\item Rajan claims there is an error in the data recorded in the table for one of the Toyotas from the South West, because there is no value for its carbon monoxide emissions.
Use your knowledge of the Large Data Set to comment on Rajan's claim. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 Q17 [6]}}