| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2001 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate range and interquartile range |
| Difficulty | Easy -1.2 This is a straightforward S1 statistics question requiring basic data handling skills: reading a stem-and-leaf diagram, finding quartiles from ordered data (n=46, so quartile positions are standard), and drawing box plots. All techniques are routine recall with no problem-solving or insight required, making it easier than average. |
| Spec | 2.02f Measures of average and spread2.02i Select/critique data presentation |
| Lengths | 20 means 20 | |
| 2 | 0122 | \(( 4 )\) |
| 2 | 55667789 | \(( 7 )\) |
| 3 | 012224 | \(( 5 )\) |
| 3 | 566679 | \(( 5 )\) |
| 4 | 01333333444 | \(( 10 )\) |
| 4 | 5556667788999 | \(( 12 )\) |
| 5 | 000 | \(( 3 )\) |
| Diane | Gopal | |
| Smallest value | 35 | 25 |
| Lower quartile | 37 | 34 |
| Median | 42 | 42 |
| Upper quartile | 53 | 50 |
| Largest value | 65 | 57 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(Q_1 = 30\); \(Q_2 = \frac{1}{2}(41+43) = 42\); \(Q_3 = 46\) | B1, M1A1, B1 (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Box plot with scales and labels | B1 | Scales & labels |
| Box plot drawn | M1 | Box plot |
| Alan: \(30, 42, 46\); whiskers \(20, 50\) | A1\(\checkmark\), A1 (4) | |
| Diane: \(37, 42, 53\); whiskers \(35, 65\) | B1, B1\(\checkmark\) (2) | |
| Gopal: \(34, 42, 50\); whiskers \(25, 57\) | B1, B1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Alan — negative skew | B1 | |
| Diane — positive skew | B1 | |
| Gopal — symmetrical | B1 | |
| All same median; all same IQR | B1 | |
| Any other comment e.g. Diane tends to have more lengths than the other two | B1 (4) |
## Question 6:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $Q_1 = 30$; $Q_2 = \frac{1}{2}(41+43) = 42$; $Q_3 = 46$ | B1, M1A1, B1 (4) | |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Box plot with scales and labels | B1 | Scales & labels |
| Box plot drawn | M1 | Box plot |
| Alan: $30, 42, 46$; whiskers $20, 50$ | A1$\checkmark$, A1 (4) | |
| Diane: $37, 42, 53$; whiskers $35, 65$ | B1, B1$\checkmark$ (2) | |
| Gopal: $34, 42, 50$; whiskers $25, 57$ | B1, B1 (2) | |
### Part (c)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Alan — negative skew | B1 | |
| Diane — positive skew | B1 | |
| Gopal — symmetrical | B1 | |
| All same median; all same IQR | B1 | |
| Any other comment e.g. Diane tends to have more lengths than the other two | B1 (4) | |
---6. Three swimmers Alan, Diane and Gopal record the number of lengths of the swimming pool they swim during each practice session over several weeks. The stem and leaf diagram below shows the results for Alan.
\begin{center}
\begin{tabular}{ r | l l }
Lengths & 20 means 20 & \\
\hline
2 & 0122 & $( 4 )$ \\
2 & 55667789 & $( 7 )$ \\
3 & 012224 & $( 5 )$ \\
3 & 566679 & $( 5 )$ \\
4 & 01333333444 & $( 10 )$ \\
4 & 5556667788999 & $( 12 )$ \\
5 & 000 & $( 3 )$ \\
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find the three quartiles for Alan's results.
The table below summarises the results for Diane and Gopal.
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
& Diane & Gopal \\
\hline
Smallest value & 35 & 25 \\
\hline
Lower quartile & 37 & 34 \\
\hline
Median & 42 & 42 \\
\hline
Upper quartile & 53 & 50 \\
\hline
Largest value & 65 & 57 \\
\hline
\end{tabular}
\end{center}
\item Using the same scale and on the same sheet of graph paper draw box plots to represent the data for Alan, Diane and Gopal.
\item Compare and contrast the three box plots.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2001 Q6 [16]}}