| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 13 |
| 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 is a straightforward data interpretation question requiring basic statistical skills: drawing box plots from given five-number summaries, making standard comparisons using measures of location and spread, identifying limitations of data interpretation, and applying the outlier rule (mean ± 2 or 3 standard deviations). All values are provided, requiring only routine application of AS-level statistical concepts with no problem-solving or novel insight. |
| Spec | 2.02f Measures of average and spread |
| n | 32 |
| Mean | 84.2313 |
| s | 1.1563 |
| \(\sum x\) | 2695.4 |
| \(\sum x ^ { 2 }\) | 227078.36 |
| Min | 82.1 |
| Q1 | 83.45 |
| Median | 84 |
| Q3 | 84.9 |
| Max | 86.7 |
| n | 32 |
| Mean | 80.2844 |
| s | 1.4294 |
| \(\sum x\) | 2569.1 |
| \(\sum x ^ { 2 }\) | 206321.93 |
| Min | 77.6 |
| Q1 | 79 |
| Median | 80.25 |
| Q3 | 81.15 |
| Max | 83.3 |
| Answer | Marks | Guidance |
|---|---|---|
| Correct structure for two boxplots seen | B1 | Through template circles |
| Range correct and clear on one diagram | B1 | F: 82.1 to 86.7 M: 77.6 to 83.3 |
| IQR correct and clear on one diagram | B1 | F: 83.45 to 84.9 M: 79 to 81.15 |
| Median correct and clear on one diagram | B1 | F: 84 M: 80.25 |
| Both boxplots completely correct with all details | B1 | F/M label or with key |
| Answer | Marks | Guidance |
|---|---|---|
| \(80.25 < 84\) so typical male has lower life expectancy than typical female | E1 | OR \(80.2844 < 84.2313\) so the average life expectancy is lower for males; or median (or mean) life expectancy for males is less than for females |
| \(2.15 > 1.45\) OR \(5.7 > 4.6\) so life expectancy of males is more variable | E1 | OR \(1.4294 > 1.1563\) so life expectancy of males is more variable; or life expectancy for males is more variable than for females + ref to range, IQR or sd |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. The LDS deals with averages, not individuals, so it does not mean that everyone in London has a longer life expectancy than everyone in Lancashire | E1 | Any two valid different comments |
| e.g. There is no info available for Lancashire | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Either M: \(80.2844 \pm 2 \times 1.4294\ (= 83.1432)\) or F: \(84.2313 \pm 2 \times 1.1563\ (= 86.5439)\) | M1 | Correct use of criterion; \(83.1(432)\) or \(81.9(187)\) or \(86.5(439)\) or \(77.4(256)\) |
| \(83.1(432) < 83.3\) and \(86.5(439) < 86.7\) | A1 | Both correct comparisons |
| Answer | Marks |
|---|---|
| (linear) correlation | M1 |
| (strong) positive | A1 |
# Question 6:
## Part (a):
Correct structure for two boxplots seen | B1 | Through template circles
Range correct and clear on one diagram | B1 | F: 82.1 to 86.7 M: 77.6 to 83.3
IQR correct and clear on one diagram | B1 | F: 83.45 to 84.9 M: 79 to 81.15
Median correct and clear on one diagram | B1 | F: 84 M: 80.25
Both boxplots completely correct with all details | B1 | F/M label or with key
## Part (b):
$80.25 < 84$ so typical male has lower life expectancy than typical female | E1 | OR $80.2844 < 84.2313$ so the average life expectancy is lower for males; or median (or mean) life expectancy for males is less than for females
$2.15 > 1.45$ OR $5.7 > 4.6$ so life expectancy of males is more variable | E1 | OR $1.4294 > 1.1563$ so life expectancy of males is more variable; or life expectancy for males is more variable than for females + ref to range, IQR or sd
## Part (c):
e.g. The LDS deals with averages, not individuals, so it does not mean that everyone in London has a longer life expectancy than everyone in Lancashire | E1 | Any two valid different comments
e.g. There is no info available for Lancashire | E1 |
## Part (d):
Either M: $80.2844 \pm 2 \times 1.4294\ (= 83.1432)$ or F: $84.2313 \pm 2 \times 1.1563\ (= 86.5439)$ | M1 | Correct use of criterion; $83.1(432)$ or $81.9(187)$ or $86.5(439)$ or $77.4(256)$
$83.1(432) < 83.3$ and $86.5(439) < 86.7$ | A1 | Both correct comparisons
## Part (e):
(linear) **correlation** | M1 |
(strong) **positive** | A1 |
---6 The large data set gives information about life expectancy at birth for males and females in different London boroughs. Fig. 6.1 shows summary statistics for female life expectancy at birth for the years 2012-2014. Fig. 6.2 shows summary statistics for male life expectancy at birth for the years 2012-2014.
\section*{Female Life Expectancy at Birth}
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|}
\hline
n & 32 \\
\hline
Mean & 84.2313 \\
\hline
s & 1.1563 \\
\hline
$\sum x$ & 2695.4 \\
\hline
$\sum x ^ { 2 }$ & 227078.36 \\
\hline
Min & 82.1 \\
\hline
Q1 & 83.45 \\
\hline
Median & 84 \\
\hline
Q3 & 84.9 \\
\hline
Max & 86.7 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 6.1}
\end{center}
\end{table}
Male Life Expectancy at Birth
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|}
\hline
n & 32 \\
\hline
Mean & 80.2844 \\
\hline
s & 1.4294 \\
\hline
$\sum x$ & 2569.1 \\
\hline
$\sum x ^ { 2 }$ & 206321.93 \\
\hline
Min & 77.6 \\
\hline
Q1 & 79 \\
\hline
Median & 80.25 \\
\hline
Q3 & 81.15 \\
\hline
Max & 83.3 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 6.2}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Use the information in Fig. 6.1 and Fig. 6.2 to draw two box plots. Draw one box plot for female life expectancy at birth in London boroughs and one box plot for male life expectancy at birth in London boroughs.
\item Compare and contrast the distribution of male life expectancy at birth with the distribution of female life expectancy at birth in London boroughs in 2012-2014.
Lorraine, who lives in Lancashire, says she wishes her daughter (who was born in 2013) had been born in the London borough of Barnet, because her daughter would have had a higher life expectancy.
\item Give two reasons why there is no evidence in the large data set to support Lorraine's comment.
\item Use the mean and standard deviation for the summary statistics given in Fig. 6.1 and Fig. 6.2 to show that there is at least one outlier in each set.
The scatter diagram in Fig. 6.3 shows male life expectancy at birth plotted against female life expectancy at birth for London boroughs in 2012-14. The outliers have been removed.
Male life expectancy at birth against female life expectancy at birth
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{11e5167f-9f95-4494-9b66-b59fdce8b1ef-5_593_1054_1260_246}
\captionsetup{labelformat=empty}
\caption{Fig. 6.3}
\end{center}
\end{figure}
\item Describe the association between male life expectancy at birth and female life expectancy at birth in London boroughs in 2012-14.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2019 Q6 [13]}}