| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate range and interquartile range |
| Difficulty | Easy -1.3 This is a straightforward S1 question requiring basic data handling skills: reading a stem-and-leaf diagram, finding standard summary statistics (mode, median, quartiles), drawing a box plot, and commenting on skewness. All techniques are routine recall with no problem-solving or novel insight required. The only mild challenge is accurately counting positions for quartiles with n=42. |
| Spec | 2.02f Measures of average and spread2.02h Recognize outliers2.02i Select/critique data presentation |
| Number of daisies | \(1 \mid 1\) means 11 | ||||||||
| 1 | 1 | 2 | 2 | 3 | 4 | 4 | 4 | (7) | |
| 1 | 5 | 5 | 6 | 7 | 8 | 9 | 9 | (7) | |
| 2 | 0 | 0 | 1 | 3 | 3 | 3 | 3 | 4 | (8) |
| 2 | 5 | 5 | 6 | 7 | 9 | 9 | 9 | (7) | |
| 3 | 0 | 0 | 1 | 2 | 4 | 4 | (6) | ||
| 3 | 6 | 6 | 7 | 8 | 8 | (5) | |||
| 4 | 1 | 3 | (2) | ||||||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Mode \(= 23\) | B1 (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| For \(Q_1\): \(\frac{n}{4} = 10.5 \Rightarrow\) 11th observation \(\therefore Q_1 = 17\) | B1 | |
| For \(Q_2\): \(\frac{n}{2} = 21 \Rightarrow \frac{1}{2}\)(21st & 22nd) observations \(\therefore Q_2 = \frac{23+24}{2} = 23.5\) | M1 A1 | |
| For \(Q_3\): \(\frac{3n}{4} = 31.5 \Rightarrow\) 32nd observation \(\therefore Q_3 = 31\) | B1 (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Box plot drawn | M1 | |
| Scale & label | M1 | |
| \(Q_1, Q_2, Q_3\) correct | A1 | |
| Whiskers at 11, 43 | A1 (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| From box plot or \(Q_2 - Q_1 = 23.5 - 17 = 6.5\); \(Q_3 - Q_2 = 31 - 23.5 = 7.5\) (slight) positive skew | B1 (1) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Back-to-back stem and leaf diagram | B1 (1) | (11) |
## Question 2:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mode $= 23$ | B1 (1) | |
### Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| For $Q_1$: $\frac{n}{4} = 10.5 \Rightarrow$ 11th observation $\therefore Q_1 = 17$ | B1 | |
| For $Q_2$: $\frac{n}{2} = 21 \Rightarrow \frac{1}{2}$(21st & 22nd) observations $\therefore Q_2 = \frac{23+24}{2} = 23.5$ | M1 A1 | |
| For $Q_3$: $\frac{3n}{4} = 31.5 \Rightarrow$ 32nd observation $\therefore Q_3 = 31$ | B1 (4) | |
### Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Box plot drawn | M1 | |
| Scale & label | M1 | |
| $Q_1, Q_2, Q_3$ correct | A1 | |
| Whiskers at 11, 43 | A1 (4) | |
### Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| From box plot or $Q_2 - Q_1 = 23.5 - 17 = 6.5$; $Q_3 - Q_2 = 31 - 23.5 = 7.5$ (slight) positive skew | B1 (1) | |
### Part (e)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Back-to-back stem and leaf diagram | B1 (1) | **(11)** |
---2. A botany student counted the number of daisies in each of 42 randomly chosen areas of 1 m by 1 m in a large field. The results are summarised in the following stem and leaf diagram.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
\multicolumn{8}{|l|}{Number of daisies} & \multicolumn{2}{|r|}{$1 \mid 1$ means 11} \\
\hline
1 & 1 & 2 & 2 & 3 & 4 & 4 & 4 & & (7) \\
\hline
1 & 5 & 5 & 6 & 7 & 8 & 9 & 9 & & (7) \\
\hline
2 & 0 & 0 & 1 & 3 & 3 & 3 & 3 & 4 & (8) \\
\hline
2 & 5 & 5 & 6 & 7 & 9 & 9 & 9 & & (7) \\
\hline
3 & 0 & 0 & 1 & 2 & 4 & 4 & & & (6) \\
\hline
3 & 6 & 6 & 7 & 8 & 8 & & & & (5) \\
\hline
4 & 1 & 3 & & & & & & & (2) \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Write down the modal value of these data.
\item Find the median and the quartiles of these data.
\item On graph paper and showing your scale clearly, draw a box plot to represent these data.
\item Comment on the skewness of this distribution.
The student moved to another field and collected similar data from that field.
\item Comment on how the student might summarise both sets of raw data before drawing box plots.\\
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [11]}}