| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | November |
| Marks | 7 |
| 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 data handling skills: reading a stem-and-leaf diagram, finding median and quartiles by counting positions (n=61, so median is 31st value), and drawing box plots. The comparison requires only simple observational statements about center and spread. No complex calculations or statistical insight needed—purely procedural work well below average A-level difficulty. |
| Spec | 2.02f Measures of average and spread |
| Type \(A\) | Type \(B\) | |
| 9766433 | 2 | 1358 |
| 5544222 | 3 | 044566667889 |
| 9988876643220 | 4 | 0112368899 |
| 655432110 | 5 | 25669 |
| 9730 | 6 | 1389 |
| 874410 | 7 | 57 |
| 7666533210 | 8 | 1244 |
| 86555 | 9 | 06 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Median A = 0.52; LQ = 0.41; UQ = 0.79 | B1 B1 B1 | ft wrong units |
| 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Box A diagram | B1 | 2 correct boxes ft (i) OK if superimposed |
| Box B diagram | B1 | 2 pairs correct whiskers lines up to box not inside |
| Scale | B1 | Correct uniform scale need at least 4 values on it. No scale no marks unless perfect A and B with all 10 values shown, in which case score B1B1B0 |
| 3 marks | ||
| (iii) Smartphone B is quicker, slightly less variable, etc. | B1 | 1 mark; oe sensible answer |
**(i)** Median A = 0.52; LQ = 0.41; UQ = 0.79 | B1 B1 B1 | ft wrong units |
| | | 3 marks |
**(ii)**
| **Box A diagram** | B1 | 2 correct boxes ft (i) OK if superimposed |
| **Box B diagram** | B1 | 2 pairs correct whiskers lines up to box not inside |
| **Scale** | B1 | Correct uniform scale need at least 4 values on it. No scale no marks unless perfect A and B with all 10 values shown, in which case score B1B1B0 |
| | | 3 marks |
**(iii)** Smartphone B is quicker, slightly less variable, etc. | B1 | 1 mark; oe sensible answer |
---4 The following back-to-back stem-and-leaf diagram shows the times to load an application on 61 smartphones of type $A$ and 43 smartphones of type $B$.\\
(7)
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Type $A$ & & Type $B$ \\
\hline
9766433 & 2 & 1358 \\
\hline
5544222 & 3 & 044566667889 \\
\hline
9988876643220 & 4 & 0112368899 \\
\hline
655432110 & 5 & 25669 \\
\hline
9730 & 6 & 1389 \\
\hline
874410 & 7 & 57 \\
\hline
7666533210 & 8 & 1244 \\
\hline
86555 & 9 & 06 \\
\hline
\end{tabular}
\end{center}
Key: 3 | 2 | 1 means 0.23 seconds for type $A$ and 0.21 seconds for type $B$.\\
(i) Find the median and quartiles for smartphones of type $A$.
You are given that the median, lower quartile and upper quartile for smartphones of type $B$ are 0.46 seconds, 0.36 seconds and 0.63 seconds respectively.\\
(ii) Represent the data by drawing a pair of box-and-whisker plots in a single diagram on graph paper.\\
(iii) Compare the loading times for these two types of smartphone.
\hfill \mbox{\textit{CAIE S1 2014 Q4 [7]}}