| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | State advantages of diagram types |
| Difficulty | Easy -1.8 This question tests basic recall of box plot features and interpretation of standard statistical diagrams. All parts require straightforward reading of values from a given box plot, stating definitions (quartiles, outliers), and drawing a simple box plot from given five-number summary. No calculations or problem-solving required—purely descriptive statistics at the most elementary level. |
| Spec | 2.02h Recognize outliers2.02i Select/critique data presentation |
| Answer | Marks |
|---|---|
| Indicates max / median / min / upper quartile / lower quartile (2 or more) | B1 |
| Indicates outliers (or equivalent description) | B1 |
| Illustrates skewness (or equivalent description e.g. shape) - Any 3 rows | B1 |
| Allows comparisons | |
| Indicates range / IQR / spread | |
| 37 (minutes) | B1 |
| Upper quartile or \(Q_3\) or third quartile or \(75^{\text{th}}\) percentile or \(P_{75}\) | B1 |
| Outliers: How to calculate correctly; 'Observations that are very different from the other observations and need to be treated with caution'; These two children probably walked / took a lot longer - Any 2 | B1, B1 |
| Box & median & whiskers | M1 |
| Sensible scale | B1 |
| 30, 37, 50 | B1 |
| 25, 55 | B1 |
| Children from school A generally took less time - Any correct 4 lines | B1 |
| 50% of B \(\leq\) 37 mins, 75% of A < 37 mins (similarly for 30) | B1 |
| Median/Q1/Q3 of A < median/Q1/Q3 of B (1 or more) | B1 |
| A has outliers, (B does not) | B1 |
| Both positive skew | |
| IQR of A < IQR of B, range of A > range of B |
| Indicates max / median / min / upper quartile / lower quartile (2 or more) | B1 |
| Indicates outliers (or equivalent description) | B1 |
| Illustrates skewness (or equivalent description e.g. shape) - Any 3 rows | B1 |
| Allows comparisons | |
| Indicates range / IQR / spread | |
| 37 (minutes) | B1 |
| Upper quartile or $Q_3$ or third quartile or $75^{\text{th}}$ percentile or $P_{75}$ | B1 |
| Outliers: How to calculate correctly; 'Observations that are very different from the other observations and need to be treated with caution'; These two children probably walked / took a lot longer - Any 2 | B1, B1 |
| Box & median & whiskers | M1 |
| Sensible scale | B1 |
| 30, 37, 50 | B1 |
| 25, 55 | B1 |
| Children from school A generally took less time - Any correct 4 lines | B1 |
| 50% of B $\leq$ 37 mins, 75% of A < 37 mins (similarly for 30) | B1 |
| Median/Q1/Q3 of A < median/Q1/Q3 of B (1 or more) | B1 |
| A has outliers, (B does not) | B1 |
| Both positive skew | |
| IQR of A < IQR of B, range of A > range of B | |
**Total 15 marks**
---\begin{enumerate}
\item (a) Describe the main features and uses of a box plot.\\
\end{enumerate}
Children from schools $A$ and $B$ took part in a fun run for charity. The times, to the nearest minute, taken by the children from school $A$ are summarised in Figure 1.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{c8bade79-a39a-4055-bfae-928f5338fdfc-02_398_1045_946_461}
\end{center}
\end{figure}
(b) (i) Write down the time by which $75 \%$ of the children in school $A$ had completed the run.\\
(ii) State the name given to this value.\\
(c) Explain what you understand by the two crosses ( X ) on Figure 1.\\
For school $B$ the least time taken by any of the children was 25 minutes and the longest time was 55 minutes. The three quartiles were 30,37 and 50 respectively.\\
(d) Draw a box plot to represent the data from school $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{c8bade79-a39a-4055-bfae-928f5338fdfc-03_798_1196_580_372}\\
(e) Compare and contrast these two box plots.\\
\hfill \mbox{\textit{Edexcel S1 2006 Q1 [15]}}