| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct stem-and-leaf then find median and quartiles |
| Difficulty | Easy -1.3 This is a straightforward data handling question requiring only routine procedures: constructing a stem-and-leaf diagram from ordered data, finding the median (middle value of 27 items), calculating quartiles using standard position formulas, and drawing a box plot. All techniques are mechanical with no problem-solving or conceptual challenge beyond basic statistical literacy. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| 104 | 88 | 82 | 65 | 44 | 38 | 35 | 34 | 28 |
| 28 | 18 | 18 | 17 | 17 | 14 | 13 | 13 | 12 |
| 12 | 10 | 10 | 10 | 9 | 6 | 5 | 2 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Stem drawn | B1 | Stem, digits 5, 7, 9 can be missing here, can be upside down |
| \(0\ \ | \ 2\ 2\ 5\ 6\ 9\) and \(1\ \ | \ 0\ 0\ 0\ 2\ 2\ 3\ 3\ 4\ 7\ 7\ 8\ 8\) etc. |
| Reasonable shape, all stems present | B1 | Reasonable shape, requires all values of stem, only one line for each stem and leaves must be lined up. Can be upside down or sideways. No commas. Condone one 'leaf' error. |
| key \(2\ \ | \ 8\) means 28 medals | B1 |
| 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\text{Med} = 17\) | B1 | Median correct |
| \(LQ = 10,\ UQ = 35\) | B1 | LQ and UQ correct |
| Uniform scale from 2 to 104, labelled | B1 | Uniform scale from 2 to 104 (need 3 identified points min) and label including medals (can be in title) |
| Box with med and quartiles correct | B1 FT | Correct box med and quartiles on diagram, FT their values |
| Whiskers from ends of box | B1 | Correct end-whiskers from ends of box but not through box |
| 5 |
## Question 5(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| Stem drawn | B1 | Stem, digits 5, 7, 9 can be missing here, can be upside down |
| $0\ \|\ 2\ 2\ 5\ 6\ 9$ and $1\ \|\ 0\ 0\ 0\ 2\ 2\ 3\ 3\ 4\ 7\ 7\ 8\ 8$ etc. | B1 | All leaves in correct order increasing from stem, (5, 7 and 9 can be missing), condone commas |
| Reasonable shape, all stems present | B1 | Reasonable shape, requires all values of stem, only one line for each stem and leaves must be lined up. Can be upside down or sideways. No commas. Condone one 'leaf' error. |
| key $2\ \|\ 8$ means 28 medals | B1 | Correct key must state 'medals' or have 'medals' in leaf heading or title |
| | **4** | |
---
## Question 5(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{Med} = 17$ | B1 | Median correct |
| $LQ = 10,\ UQ = 35$ | B1 | LQ and UQ correct |
| Uniform scale from 2 to 104, labelled | B1 | Uniform scale from 2 to 104 (need 3 identified points min) and label including medals (can be in title) |
| Box with med and quartiles correct | B1 FT | Correct box med and quartiles on diagram, FT their values |
| Whiskers from ends of box | B1 | Correct end-whiskers from ends of box but not through box |
| | **5** | |
---5 The number of Olympic medals won in the 2012 Olympic Games by the top 27 countries is shown below.
\begin{center}
\begin{tabular}{ r r r r r r r r r }
104 & 88 & 82 & 65 & 44 & 38 & 35 & 34 & 28 \\
28 & 18 & 18 & 17 & 17 & 14 & 13 & 13 & 12 \\
12 & 10 & 10 & 10 & 9 & 6 & 5 & 2 & 2 \\
\end{tabular}
\end{center}
(i) Draw a stem-and-leaf diagram to illustrate the data.\\
(ii) Find the median and quartiles and draw a box-and-whisker plot on the grid.\\
\includegraphics[max width=\textwidth, alt={}, center]{4c2afa86-960c-473e-970c-ed16c8434fec-07_1006_1406_1007_411}
\hfill \mbox{\textit{CAIE S1 2017 Q5 [9]}}