| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.3 This is a straightforward S1 question requiring routine application of standard procedures: reading from a stem-and-leaf diagram, finding median/quartiles by position, calculating IQR, and applying a given outlier formula. All steps are mechanical with no problem-solving or conceptual insight required, making it easier than average A-level questions. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Number of seedlings | (2 | 1 means 21) | Totals |
| 0 | 02 | (2) |
| 0 | (0) | |
| 1 | 1 | (1) |
| 1 | 57 | (2) |
| 2 | 01334 | (5) |
| 2 | 5777899 | (7) |
| 3 | 0001224 | (7) |
| 3 | 5688 | (4) |
| 4 | 134 | (3) |
| Answer | Marks |
|---|---|
| \(n = 31\), median = 29 | A1 |
| \(Q_1 = 23\) | A1 |
| \(Q_3 = 34\) | A1 |
| \(\text{IQR} = Q_3 - Q_1 = 34 - 23 = 11\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(Q_2 - Q_1 = 6\); \(Q_3 - Q_2 = 5\) | M1 |
| \(\therefore Q_3 - Q_1 > Q_3 - Q_2 \therefore\) slight +ve skew | M1 A1 |
| Answer | Marks |
|---|---|
| e.g. recommend mean and std. dev. as they take account of all values and there is little skew / few extreme values | B2 |
| Answer | Marks |
|---|---|
| \(Q_1 - 2x = 2.4\); \(Q_3 + 2x = 54.6 \therefore\) outliers are 0, 2 | M1 A1 |
| Boxplot | B4 |
| (16) |
**Part (a)**
$n = 31$, median = 29 | A1 |
$Q_1 = 23$ | A1 |
$Q_3 = 34$ | A1 |
$\text{IQR} = Q_3 - Q_1 = 34 - 23 = 11$ | M1 A1 |
**Part (b)**
$Q_2 - Q_1 = 6$; $Q_3 - Q_2 = 5$ | M1 |
$\therefore Q_3 - Q_1 > Q_3 - Q_2 \therefore$ slight +ve skew | M1 A1 |
**Part (c)**
e.g. recommend mean and std. dev. as they take account of all values and there is little skew / few extreme values | B2 |
**Part (d)**
$Q_1 - 2x = 2.4$; $Q_3 + 2x = 54.6 \therefore$ outliers are 0, 2 | M1 A1 |
**Boxplot** | B4 |
| (16) |5. Each child in class 3A was given a packet of seeds to plant. The stem and leaf diagram below shows how many seedlings were visible in each child's tray one week after planting.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Number of seedlings & (2 | 1 means 21) & Totals \\
\hline
0 & 02 & (2) \\
\hline
0 & & (0) \\
\hline
1 & 1 & (1) \\
\hline
1 & 57 & (2) \\
\hline
2 & 01334 & (5) \\
\hline
2 & 5777899 & (7) \\
\hline
3 & 0001224 & (7) \\
\hline
3 & 5688 & (4) \\
\hline
4 & 134 & (3) \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find the median and interquartile range for these data.
\item Use the quartiles to describe the skewness of the data. Show your method clearly.
The mean and standard deviation for these data were 27.2 and 10.3 respectively.
\item Explaining your answer, state whether you would recommend using these values or your answers to part (a) to summarise these data.
Outliers are defined to be values outside of the limits $\mathrm { Q } _ { 1 } - 2 s$ and $\mathrm { Q } _ { 3 } + 2 s$ where $s$ is the standard deviation given above.
\item Represent these data with a boxplot identifying clearly any outliers.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [16]}}