| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from large data set |
| Difficulty | Easy -1.2 This is a straightforward multi-part question testing basic statistical calculations (mean, standard deviation) and outlier identification using a simple rule. All parts involve routine procedures with small datasets requiring no problem-solving insight, though part (a) requires knowledge of the Large Data Set context which is curriculum-specific recall. |
| Spec | 2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Electric/petrol (hybrid or Category 8) | B1 | Only category with this many values |
| Only category with more than one value | E1 | Accept only other category with more than one value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(72.375\) | B1 | AWRT 72.4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(28.7\) | B1 | Accept 26.8; AWRT for either value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(72.4 - 2 \times 28.7 \approx 15 > 13\) | R1 | Calculates AWRT \(72.4 - 2 \times s.d.\) and shows value greater than 13 obtained. Using 26.8 gives 18.8 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Standard deviation will decrease | R1 | Infers standard deviation/it will decrease. Accept one word answers. Ignore any calculations unless contradictory |
## Question 13(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Electric/petrol (hybrid or Category 8) | B1 | Only category with this many values |
| Only category with more than one value | E1 | Accept only other category with more than one value |
## Question 13(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $72.375$ | B1 | AWRT 72.4 |
## Question 13(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $28.7$ | B1 | Accept 26.8; AWRT for either value |
## Question 13(d)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $72.4 - 2 \times 28.7 \approx 15 > 13$ | R1 | Calculates AWRT $72.4 - 2 \times s.d.$ and shows value greater than 13 obtained. Using 26.8 gives 18.8 |
## Question 13(d)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Standard deviation will decrease | R1 | Infers standard deviation/it will decrease. Accept one word answers. Ignore any calculations unless contradictory |
---13 Denzel wants to buy a car with a propulsion type other than petrol or diesel.\\
He takes a sample, from the Large Data Set, of the CO2 emissions, in $\mathrm { g } / \mathrm { km }$, of cars with one particular propulsion type.
The sample is as follows
$$\begin{array} { l l l l l l l l }
82 & 13 & 96 & 49 & 96 & 92 & 70 & 81
\end{array}$$
13
\begin{enumerate}[label=(\alph*)]
\item Using your knowledge of the Large Data Set, state which propulsion type this sample is for, giving a reason for your answer.\\
13
\item Calculate the mean of the sample.\\
13
\item Calculate the standard deviation of the sample.\\
13
\item Denzel claims that the value 13 is an outlier.
13 (d) (i) Any value more than 2 standard deviations from the mean can be regarded as an outlier.
Verify that Denzel's claim is correct.\\
13 (d) (ii) State what effect, if any, removing the value 13 from the sample would have on the standard deviation.
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2019 Q13 [6]}}