| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2023 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Identify outliers using IQR rule |
| Difficulty | Moderate -0.8 This is a straightforward statistics question testing basic concepts: outlier detection using the 1.5×IQR rule (routine calculation), identifying an outlier by name (recall), finding k from a probability distribution (simple algebra), and describing quota sampling (recall of theory). All parts are standard textbook exercises requiring no problem-solving insight, making it easier than average. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.02f Measures of average and spread2.02h Recognize outliers |
| \(n\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 or more |
| \(P(N = n)\) | 0.14 | 0.37 | 0.9k | 0.25 | 0.4k | 1.7k | 0 |
| Answer | Marks |
|---|---|
| 15(a)(i) | Finds IQR |
| Answer | Marks | Guidance |
|---|---|---|
| value for the lower or upper limit | 1.1 b | B 1 |
| Answer | Marks | Guidance |
|---|---|---|
| or upper limit | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| limits and selects mass 2040 | 3.2a | A1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 15(a)(ii) | States ‘outlier’ | |
| ISW | 1.2 | B1 |
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 15(b) | Forms the equation for total |
| Answer | Marks | Guidance |
|---|---|---|
| PI by k = 0.08 OE | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 1.1a | M1 |
| Obtains correct probability | 1.1b | A1 |
| Subtotal | 4 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 15(c)(i) | Identifies the LDS contains cars |
| Answer | Marks | Guidance |
|---|---|---|
| car or 10 groups | 2.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| for both years | 2.4 | R1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 15(c)(ii) | States that the disadvantage of |
| Answer | Marks | Guidance |
|---|---|---|
| proportionate. | 3.5b | E1 |
| Subtotal | 1 | |
| Question 15 Total | 11 | |
| Q | Marking instructions | AO |
Question 15:
--- 15(a)(i) ---
15(a)(i) | Finds IQR
PI by correct expression or
value for the lower or upper limit | 1.1 b | B 1 | IQR = 1570 – 1167 = 403
1393 – 1.5 × 403 = 788.5
1393 + 1.5 × 403 = 1997.5
Hence 2040 should be removed
Substitutes their IQR and
obtains a value for the lower or
upper limit
PI by correct value for the lower
or upper limit | 1.1a | M1
Obtains correct lower and upper
limits and selects mass 2040 | 3.2a | A1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 15(a)(ii) ---
15(a)(ii) | States ‘outlier’
ISW | 1.2 | B1 | Outlier
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 15(b) ---
15(b) | Forms the equation for total
probability
PI by k = 0.08 OE | 3.1b | M1 | 0.14 + 0.37 + 0.9k + 0.25 +
0.4k + 1.7k = 1
0.76 + 3k = 1
k = 0.08
P(1 ≤ N < 5) = 0.37 + 0.9 × 0.08 +
0.25 + 0.4 × 0.08
= 0.724
Obtains the correct value of k
OE | 1.1b | A1
Forms a correct expression for
P(1 ≤ N < 5) with or without k
substituted
e.g 0.37 + 0.9k + 0.25 + 0.4k
or 0.62 + 1.3k or
1– 0.14 – 1.7k
OE | 1.1a | M1
Obtains correct probability | 1.1b | A1
Subtotal | 4
Q | Marking instructions | AO | Marks | Typical solution
--- 15(c)(i) ---
15(c)(i) | Identifies the LDS contains cars
from 2 years or chooses 100
cars from each year
or identifies the LDS contains 5
makes of car or chooses 40
from each make
Condone statement 20 of each
car or 10 groups | 2.4 | M1 | Select 20 of each of the five makes
of car in each of the two years.
Concludes that 20 cars selected
from each of the 5 makes of car
for both years | 2.4 | R1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 15(c)(ii) ---
15(c)(ii) | States that the disadvantage of
quota sampling in LDS is that it
is biased or not random or not
proportionate. | 3.5b | E1 | Could produce a biased sample
Subtotal | 1
Question 15 Total | 11
Q | Marking instructions | AO | Marks | Typical solution\begin{enumerate}[label=(\alph*)]
\item A random sample of eight cars was selected from the Large Data Set.
The masses of these cars, in kilograms, were as follows.
950 989 1247 1415 1506 1680 1833 2040
It is given that, for the population of cars in the Large Data Set:
lower quartile = 1167
median = 1393
upper quartile = 1570
\begin{enumerate}[label=(\roman*)]
\item It was decided to remove any of the masses which fall outside the following interval.
median $- 1.5 \times$ interquartile range $\leq$ mass $\leq$ median $+ 1.5 \times$ interquartile range
Show that only one of the eight masses in the sample should be removed.
[3 marks]
\item Write down the statistical name for the mass that should be removed in part (a)(i).
[1 mark]
\end{enumerate}
\item The table shows the probability distribution of the number of previous owners, $N$, for a sample of cars taken from the Large Data Set.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
$n$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 or more \\
\hline
$P(N = n)$ & 0.14 & 0.37 & 0.9k & 0.25 & 0.4k & 1.7k & 0 \\
\hline
\end{tabular}
\end{center}
Find the value of $P(1 \leq N < 5)$
[4 marks]
\item An expert team is investigating whether there have been any changes in CO₂ emissions from all cars taken from the Large Data Set.
The team decided to collect a quota sample of 200 cars to reflect the different years and the different makes of cars in the Large Data Set.
\begin{enumerate}[label=(\roman*)]
\item Using your knowledge of the Large Data Set, explain how the team can collect this sample.
[2 marks]
\item Describe one disadvantage of quota sampling.
[1 mark]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2023 Q15 [11]}}