| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct back-to-back stem-and-leaf from raw data |
| Difficulty | Easy -1.2 This is a straightforward data handling question requiring routine construction of a stem-and-leaf diagram and calculation of standard summary statistics from small datasets. All techniques are basic S1 content with no problem-solving or insight required—purely mechanical application of learned procedures. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Dados | 6 | 8 | 12 | 15 | 10 | 36 | 42 | 28 | 10 | 22 | 16 |
| Linva | 2 | 11 | 15 | 16 | 0 | 32 | 36 | 40 | 10 | 12 | 9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct stem (can be upside down, ignore extra values) | B1 | Stem can be upside down |
| Correct Dados labelled, leaves in order and lined up vertically, no commas, no extra terms | B1 | Less than midway to next column |
| Correct Linva on opposite side of stem labelled, leaves in order and lined up vertically, no commas, no extra terms | B1 | Less than midway to next column |
| KEY: \(6\ | 3\ | 2\) means 36 cm (snow) in Dados and 32 cm (snow) in Linva |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median or \(Q_2 = 15\) (cm) | B1 | Correct |
| \(UQ\) or \(Q_3 = 28\) cm, \(LQ\) or \(Q_1 = 10\) cm; \(IQR = 28 - 10\) | M1 | \(22 \leqslant UQ \leqslant 36 - 8 \leqslant LQ \leqslant 10\) |
| 18 (cm) | A1 | WWW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| On average the snowfall in Davos is higher | B1 FT | FT from their 5(b) values for Dados. Statement comparing central tendency in context |
| The amount of snowfall in Linva varies more than in Davos | B1 FT | Statement comparing spread in context. Simply stating and comparing values is not sufficient |
# Question 5(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct stem (can be upside down, ignore extra values) | B1 | Stem can be upside down |
| Correct Dados labelled, leaves in order and lined up vertically, no commas, no extra terms | B1 | Less than midway to next column |
| Correct Linva on opposite side of stem labelled, leaves in order and lined up vertically, no commas, no extra terms | B1 | Less than midway to next column |
| KEY: $6\|3\|2$ means 36 cm (snow) in Dados and 32 cm (snow) in Linva | B1 | Need both resorts identified and 'cm' stated at least once. SC: if 2 separate diagrams drawn, SCB1 if both keys meet criteria. B0B1B0SCB1 max |
# Question 5(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median or $Q_2 = 15$ (cm) | B1 | Correct |
| $UQ$ or $Q_3 = 28$ cm, $LQ$ or $Q_1 = 10$ cm; $IQR = 28 - 10$ | M1 | $22 \leqslant UQ \leqslant 36 - 8 \leqslant LQ \leqslant 10$ |
| 18 (cm) | A1 | WWW |
# Question 5(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| On average the snowfall in Davos is higher | B1 FT | FT from their 5(b) values for Dados. Statement comparing central tendency in context |
| The amount of snowfall in Linva varies more than in Davos | B1 FT | Statement comparing spread in context. Simply stating and comparing values is not sufficient |5 The following table gives the weekly snowfall, in centimetres, for 11 weeks in 2018 at two ski resorts, Dados and Linva.
\begin{center}
\begin{tabular}{ | l | r | r | r | r | r | r | r | r | r | r | r | }
\hline
Dados & 6 & 8 & 12 & 15 & 10 & 36 & 42 & 28 & 10 & 22 & 16 \\
\hline
Linva & 2 & 11 & 15 & 16 & 0 & 32 & 36 & 40 & 10 & 12 & 9 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Represent the information in a back-to-back stem-and-leaf diagram.
\item Find the median and the interquartile range for the weekly snowfall in Dados.
\item The median, lower quartile and upper quartile of the weekly snowfall for Linva are 12, 9 and 32 cm respectively. Use this information and your answers to part (b) to compare the central tendency and the spread of the weekly snowfall in Dados and Linva.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2020 Q5 [9]}}