| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2019 |
| Session | June |
| 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 -0.3 This is a straightforward statistics question requiring calculation of mean and standard deviation to identify an outlier using the 2SD rule, followed by conceptual understanding of how removing an outlier affects summary statistics. The calculations are routine (10 data points, simple arithmetic) and the concepts are standard A-level content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Rower | Jess | Nell | Liv | Neve | Ann | Tori | Maya | Kath | Darcy | Jen |
| Height (cm) | 162 | 169 | 172 | 156 | 146 | 161 | 159 | 164 | 157 | 160 |
| Answer | Marks | Guidance |
|---|---|---|
| 12(a) | Calculates correct value of mean | |
| (accept 161) | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| (accept 7.2 or better) | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| οΏ½π₯π₯ 2Γπ π .ππ | 1.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| FT their and their s.d | 2.1 | R1F |
| Answer | Marks |
|---|---|
| 12(b) | States co οΏ½π₯π₯rrectly that the mean |
| Answer | Marks | Guidance |
|---|---|---|
| reason | 2.2b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| reason | 2.2b | B1 |
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 12:
--- 12(a) ---
12(a) | Calculates correct value of mean
(accept 161) | 1.1b | B1 | x =160.6
sd = 6.8
160.6 β 2 Γ 6.8 = 147
146 < 147
Hence Ann is an outlier
Calculates correct value of
standard deviation
(accept 7.2 or better) | 1.1b | B1
Uses in
β
(acceptht e1i4r 6οΏ½π₯π₯. 2ππ)ππ ππ their π π .ππ
οΏ½π₯π₯ 2Γπ π .ππ | 1.1b | M1
Compares 146 with their
calculation and correctly
concludes that Annβs height is an
outlier
FT their and their s.d | 2.1 | R1F
--- 12(b) ---
12(b) | States co οΏ½π₯π₯rrectly that the mean
would increase with a valid
reason or
increases to 162.2
Accept the mean would increase
as the lower/lowest value has
been removed or other valid
reason | 2.2b | B1 | The mean would increase because
Annβs height is less than the mean
Standard deviation would decrease
because Annβs height is an outlier
States correctly that the standard
deviation would decrease with a
valid reason or
decreases to 5.03
Accept the standard deviation
would decrease because the data
is less spread out or other valid
reason | 2.2b | B1
Total | 6
Q | Marking Instructions | AO | Mark | Typical SolutionAmelia decides to analyse the heights of members of her school rowing club.
The heights of a random sample of 10 rowers are shown in the table below.
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline
Rower & Jess & Nell & Liv & Neve & Ann & Tori & Maya & Kath & Darcy & Jen \\
\hline
Height (cm) & 162 & 169 & 172 & 156 & 146 & 161 & 159 & 164 & 157 & 160 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Any value more than 2 standard deviations from the mean may be regarded as an outlier.
Verify that Ann's height is an outlier.
Fully justify your answer. [4 marks]
\item Amelia thinks she may have written down Ann's height incorrectly.
If Ann's height were discarded, state with a reason what, if any, difference this would make to the mean and standard deviation. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2019 Q12 [6]}}