Question 13 - A-Level Maths

AQA Paper 3 2021 June — Question 13 6 marks

Exam Board	AQA
Module	Paper 3 (Paper 3)
Year	2021
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	Moderate -0.8 This question tests basic statistical calculations (mean, standard deviation) and outlier identification using a simple rule, plus data interpretation. The calculations are straightforward with 13 values, and the outlier check is mechanical (compare to mean ± 2SD). Part (b) requires familiarity with the Large Data Set context but is essentially spotting that mass=0 is implausible and missing particulate data is suspicious. This is below average difficulty as it's mostly routine computation and data sense rather than problem-solving.
Spec	2.02f Measures of average and spread 2.02g Calculate mean and standard deviation 2.02h Recognize outliers 2.02j Clean data: missing data, errors

The table below is an extract from the Large Data Set.

Propulsion Type	Region	Engine Size	Mass	CO₂	Particulate Emissions
2	London	1896	1533	154	0.04
2	North West	1896	1423	146	0.029
2	North West	1896	1353	138	0.025
2	South West	1998	1547	159	0.026
2	London	1896	1388	138	0.025
2	South West	1896	1214	130	0.011
2	South West	1896	1480	146	0.029
2	South West	1896	1413	146	0.024
2	South West	2496	1695	192	0.034
2	South West	1422	1251	122	0.025
2	South West	1995	2075	175	0.034
2	London	1896	1285	140	0.036
2	North West	1896	0	146

1. Calculate the mean and standard deviation of CO₂ emissions in the table. [2 marks]
2. Any value more than 2 standard deviations from the mean can be identified as an outlier. Determine, using this definition of an outlier, if there are any outliers in this sample of CO₂ emissions. Fully justify your answer. [2 marks]
Maria claims that the last line in the table must contain two errors. Use your knowledge of the Large Data Set to comment on Maria's claim. [2 marks]

Show mark scheme Show mark scheme source

Question 13:

Answer	Marks	Guidance
13(a)(i)	Calculates correct value of
mean AWRT 149	1.1b	B1

Standard deviation = 17.8

Calculates correct value of

standard deviation AWRT 17.8

Answer	Marks	Guidance
Accept AWRT 18.5	1.1b	B1
Subtotal	2
Q	Marking Instructions	AO

Answer	Marks
13(a)(ii)	Calculates either their

mean + 2 standard deviation

or their mean – 2 standard

deviation ×

Answer	Marks	Guidance
×	1.1b	M1

148.6 – 2 17.8 = 113

192 > 184.×2

192 is the ×only outlier

Deduces that the CO2 value of

192 is the only outlier – must

make a clear comparison and

have both lower and upper

outlier boundaries

FT their mean and standard

Answer	Marks	Guidance
deviation	2.2a	R1F
Subtotal	2
Q	Marking Instructions	AO

Answer	Marks
13(b)	Explains that the 0 value is an

error because every car has a

Answer	Marks	Guidance
mass or there is a driver mass	2.2b	E1

every car has a mass

The blank cell may not be an error

as not all particulate emissions are

recorded in the LDS

Explains that the blank cell may

not be an error as the LDS only

has particulate emissions

Answer	Marks	Guidance
recorded for some cars	2.2b	E1
Subtotal	2
Question Total	6
Q	Marking Instructions	AO

Question 13:
--- 13(a)(i) ---
13(a)(i) | Calculates correct value of
mean AWRT 149 | 1.1b | B1 | Mean = 148.6
Standard deviation = 17.8
Calculates correct value of
standard deviation AWRT 17.8
Accept AWRT 18.5 | 1.1b | B1
Subtotal | 2
Q | Marking Instructions | AO | Marks | Typical Solution
--- 13(a)(ii) ---
13(a)(ii) | Calculates either their
mean + 2 standard deviation
or their mean – 2 standard
deviation ×
× | 1.1b | M1 | 148.6 + 2 17.8 = 184.2
148.6 – 2 17.8 = 113
192 > 184.×2
192 is the ×only outlier
Deduces that the CO2 value of
192 is the only outlier – must
make a clear comparison and
have both lower and upper
outlier boundaries
FT their mean and standard
deviation | 2.2a | R1F
Subtotal | 2
Q | Marking Instructions | AO | Marks | Typical Solution
--- 13(b) ---
13(b) | Explains that the 0 value is an
error because every car has a
mass or there is a driver mass | 2.2b | E1 | The 0 value is an error because
every car has a mass
The blank cell may not be an error
as not all particulate emissions are
recorded in the LDS
Explains that the blank cell may
not be an error as the LDS only
has particulate emissions
recorded for some cars | 2.2b | E1
Subtotal | 2
Question Total | 6
Q | Marking Instructions | AO | Marks | Typical Solution

Show LaTeX source

The table below is an extract from the Large Data Set.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Propulsion Type & Region & Engine Size & Mass & CO₂ & Particulate Emissions \\
\hline
2 & London & 1896 & 1533 & 154 & 0.04 \\
2 & North West & 1896 & 1423 & 146 & 0.029 \\
2 & North West & 1896 & 1353 & 138 & 0.025 \\
2 & South West & 1998 & 1547 & 159 & 0.026 \\
2 & London & 1896 & 1388 & 138 & 0.025 \\
2 & South West & 1896 & 1214 & 130 & 0.011 \\
2 & South West & 1896 & 1480 & 146 & 0.029 \\
2 & South West & 1896 & 1413 & 146 & 0.024 \\
2 & South West & 2496 & 1695 & 192 & 0.034 \\
2 & South West & 1422 & 1251 & 122 & 0.025 \\
2 & South West & 1995 & 2075 & 175 & 0.034 \\
2 & London & 1896 & 1285 & 140 & 0.036 \\
2 & North West & 1896 & 0 & 146 & \\
\hline
\end{tabular}
\end{center}

\begin{enumerate}[label=(\alph*)]
\item 
\begin{enumerate}[label=(\roman*)]
\item Calculate the mean and standard deviation of CO₂ emissions in the table.
[2 marks]

\item Any value more than 2 standard deviations from the mean can be identified as an outlier.

Determine, using this definition of an outlier, if there are any outliers in this sample of CO₂ emissions.

Fully justify your answer.
[2 marks]
\end{enumerate}

\item Maria claims that the last line in the table must contain two errors.

Use your knowledge of the Large Data Set to comment on Maria's claim.
[2 marks]
\end{enumerate}

\hfill \mbox{\textit{AQA Paper 3 2021 Q13 [6]}}

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