| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw box plot from raw data |
| Difficulty | Moderate -0.8 This is a routine S1 data handling question requiring standard procedures: constructing a stem-and-leaf diagram, finding summary statistics from ordered data, and drawing boxplots. All techniques are straightforward textbook exercises with no problem-solving or interpretation challenges beyond basic comparison statements. The most demanding part is careful ordering and counting, making it easier than average. |
| 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 |
| 39 | 19 | 28 | 30 | 18 | 21 | 23 | 15 | 34 | 24 |
| 29 | 17 | 43 | 12 | 24 | 25 | 41 | 19 | 26 | 40 |
| 45 | 23 | 21 | 32 | 37 | 24 | 18 | 15 | 24 | 36 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | B3 | Stem-and-leaf diagram with correct structure and values: |
| 1 | 1 | |
| 1 | 5 5 7 8 8 9 9 | |
| 2 | 1 1 3 3 4 4 4 4 | |
| 2 | 5 6 8 9 | |
| 3 | 0 2 4 | |
| 3 | 6 7 9 | |
| 4 | 0 1 3 | |
| 4 | 5 | |
| (b) | A1 | \(Q_1 = 19\) |
| A1 | \(Q_2 = 24\) | |
| M1 A1 | \(Q_3 = 34 + \frac{1}{4}(36 - 34) = 34.5\) | |
| (c) | B3 | Box plot with correct median, quartiles and whiskers |
| (d) | B2 | Box plot with similar features to (c) |
| (e) | B3, (15) | e.g. Tahira more points on av.; Tahira more consistent (smaller IQR); Jane sometimes v. high i.e. +ve skew whereas Tahira symm. |
(a) | B3 | Stem-and-leaf diagram with correct structure and values:
| | 1 | 1 |
| | 1 | 5 5 7 8 8 9 9 |
| | 2 | 1 1 3 3 4 4 4 4 |
| | 2 | 5 6 8 9 |
| | 3 | 0 2 4 |
| | 3 | 6 7 9 |
| | 4 | 0 1 3 |
| | 4 | 5 |
(b) | A1 | $Q_1 = 19$
| A1 | $Q_2 = 24$
| M1 A1 | $Q_3 = 34 + \frac{1}{4}(36 - 34) = 34.5$
(c) | B3 | Box plot with correct median, quartiles and whiskers
(d) | B2 | Box plot with similar features to (c)
(e) | B3, (15) | e.g. Tahira more points on av.; Tahira more consistent (smaller IQR); Jane sometimes v. high i.e. +ve skew whereas Tahira symm.
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# Total: (75)Jane and Tahira play together in a basketball team. The list below shows the number of points that Jane scored in each of 30 games.
\begin{center}
\begin{tabular}{ccccccccccc}
39 & 19 & 28 & 30 & 18 & 21 & 23 & 15 & 34 & 24 \\
29 & 17 & 43 & 12 & 24 & 25 & 41 & 19 & 26 & 40 \\
45 & 23 & 21 & 32 & 37 & 24 & 18 & 15 & 24 & 36
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Construct a stem and leaf diagram for these data. [3 marks]
\item Find the median and quartiles for these data. [4 marks]
\item Represent these data with a boxplot. [3 marks]
\end{enumerate}
Tahira played in the same 30 games and her lowest and highest points total in a game were 19 and 41 respectively. The quartiles for Tahira were 27, 31 and 35 respectively.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Using the same scale draw a boxplot for Tahira's points totals. [2 marks]
\item Compare and contrast the number of points scored per game by Jane and Tahira. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q7 [15]}}