| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate range and interquartile range |
| Difficulty | Easy -1.8 This is a straightforward S1 question requiring only basic recall: reading values from a stem-and-leaf diagram to find quartiles (using the standard n/4 position method), drawing box plots from given five-number summaries, and writing simple comparative statements. No problem-solving, calculation complexity, or conceptual insight required—purely procedural application of GCSE-level statistical techniques. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| Caravans | 1 | 10 means 10 | Totals | ||
| 1 | 0 | (2) | |||
| 2 | 1 | 8 | (4) | ||
| 3 | 0 | 3 | 4 | 7 | (8) |
| 4 | 1 | 5 | 8 | 8 | (9) |
| 5 | 2 | 6 | 7 | (5) | |
| 6 | 2 | (3) | |||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(Q_1 = 33\), \(Q_2 = 41\), \(Q_3 = 52\) | B1, B1, B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Scale and labels | B1 | |
| Box plot drawn | M1 | |
| \(S_V\): \(Q_1, Q_2, Q_3\) correct; 10, 64 | A1, A1 | |
| \(N_C\): 38, 45, 52 correct | A1 | |
| 3, 79 whiskers | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median of Northcliffe is greater than median of Seaview | B1 | Any 3 acceptable comments |
| Upper quartiles are the same | B1 | |
| IQR of Northcliffe is less than IQR of Seaview | B1 | |
| Northcliffe positive skew, Seaview negative skew | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| On 75% of the nights that month | B1 | |
| Both had no more than 52 caravans on site | B1 |
# Question 2:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $Q_1 = 33$, $Q_2 = 41$, $Q_3 = 52$ | B1, B1, B1 | |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Scale and labels | B1 | |
| Box plot drawn | M1 | |
| $S_V$: $Q_1, Q_2, Q_3$ correct; 10, 64 | A1, A1 | |
| $N_C$: 38, 45, 52 correct | A1 | |
| 3, 79 whiskers | A1 | |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median of Northcliffe is greater than median of Seaview | B1 | Any 3 acceptable comments |
| Upper quartiles are the same | B1 | |
| IQR of Northcliffe is less than IQR of Seaview | B1 | |
| Northcliffe positive skew, Seaview negative skew | B1 | |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| On 75% of the nights that month | B1 | |
| Both had no more than 52 caravans on site | B1 | |
---2. The number of caravans on Seaview caravan site on each night in August last year is summarised in the following stem and leaf diagram.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{2}{|l|}{Caravans} & & 1 & 10 means 10 & Totals \\
\hline
1 & 0 & & & & (2) \\
\hline
2 & 1 & 8 & & & (4) \\
\hline
3 & 0 & 3 & 4 & 7 & (8) \\
\hline
4 & 1 & 5 & 8 & 8 & (9) \\
\hline
5 & 2 & 6 & 7 & & (5) \\
\hline
6 & 2 & & & & (3) \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find the three quartiles of these data.
During the same month, the least number of caravans on Northcliffe caravan site was 31. The maximum number of caravans on this site on any night that month was 72 . The three quartiles for this site were 38,45 and 52 respectively.
\item On graph paper and using the same scale, draw box plots to represent the data for both caravan sites. You may assume that there are no outliers.
\item Compare and contrast these two box plots.
\item Give an interpretation to the upper quartiles of these two distributions.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2005 Q2 [14]}}