| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Compare distributions using stem-and-leaf |
| Difficulty | Easy -1.2 This is a straightforward statistics question requiring basic interpretation of a stem-and-leaf diagram and calculation of summary statistics. Finding the median and quartiles from ordered data is routine (counting to positions 16, 32, 48 out of 63), and drawing box plots is a standard skill. The back-to-back format adds minimal complexity since the key is clearly explained. No problem-solving or conceptual insight required—pure procedural recall. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| People who exercise | People who do not exercise | |||
| (9) | 987643221 | 3 | 1577 | (4) |
| (12) | 988876653322 | 4 | 234458 | (6) |
| (9) | 877765331 | 5 | 1222344567889 | (13) |
| (7) | 6666432 | 6 | 12333455577899 | (14) |
| (3) | 841 | 7 | 245566788 | (9) |
| (4) | 9552 | 8 | 133467999 | (9) |
| (1) | 4 | 9 | 14558 | (5) |
| (0) | 10 | 336 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| B1 [1] | Or other suitable advantage e.g. can see the shape, mode etc. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| B1 | ||
| B1ft | ||
| B1ft [3] | ft on first answer missing the decimal point |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| For one linear numbered scale from 3 to 9.5, or two identically positioned scales | B1 | |
| For not exercise all correct on linear scale | B1ft | |
| For exercise correct on linear scale | B1 | |
| For two labels and cholesterol and scale labelled SR non linear scale max B0 B0 B0 B1 SR no graph paper lose one mark | B1 [4] |
(i) shows all the data
| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1 [1] | Or other suitable advantage e.g. can see the shape, mode etc. |
(ii) Not exercise LQ = 5.4, Median = 6.5, UQ = 8.3
| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1 | |
| | B1ft | |
| | B1ft [3] | ft on first answer missing the decimal point |
(iii)
- not ex: [diagram of box plot without exercise]
- ex: [diagram of box plot with exercise]
- Scale from 3 to 10: 3, 4, 5, 6, 7, 8, 9, 10
| Answer | Marks | Guidance |
|--------|-------|----------|
| For one linear numbered scale from 3 to 9.5, or two identically positioned scales | B1 | |
| For not exercise all correct on linear scale | B1ft | |
| For exercise correct on linear scale | B1 | |
| For two labels and cholesterol and scale labelled SR non linear scale max B0 B0 B0 B1 SR no graph paper lose one mark | B1 [4] | |
---4 The following back-to-back stem-and-leaf diagram shows the cholesterol count for a group of 45 people who exercise daily and for another group of 63 who do not exercise. The figures in brackets show the number of people corresponding to each set of leaves.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
& People who exercise & & People who do not exercise & \\
\hline
(9) & 987643221 & 3 & 1577 & (4) \\
\hline
(12) & 988876653322 & 4 & 234458 & (6) \\
\hline
(9) & 877765331 & 5 & 1222344567889 & (13) \\
\hline
(7) & 6666432 & 6 & 12333455577899 & (14) \\
\hline
(3) & 841 & 7 & 245566788 & (9) \\
\hline
(4) & 9552 & 8 & 133467999 & (9) \\
\hline
(1) & 4 & 9 & 14558 & (5) \\
\hline
(0) & & 10 & 336 & (3) \\
\hline
\end{tabular}
\end{center}
Key: 2 | 8 | 1 represents a cholesterol count of 8.2 in the group who exercise and 8.1 in the group who do not exercise.\\
(i) Give one useful feature of a stem-and-leaf diagram.\\
(ii) Find the median and the quartiles of the cholesterol count for the group who do not exercise.
You are given that the lower quartile, median and upper quartile of the cholesterol count for the group who exercise are 4.25, 5.3 and 6.6 respectively.\\
(iii) On a single diagram on graph paper, draw two box-and-whisker plots to illustrate the data.
\hfill \mbox{\textit{CAIE S1 2005 Q4 [8]}}