| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | November |
| Marks | 10 |
| 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 -1.3 This is a routine data handling question requiring basic statistical skills: organizing data into a stem-and-leaf diagram, finding median and IQR from ordered data, and making simple comparisons. All techniques are standard S1 procedures with no problem-solving or conceptual challenges beyond careful data manipulation. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Factory \(A\) | 0.049 | 0.050 | 0.053 | 0.054 | 0.057 | 0.058 | 0.058 |
| 0.059 | 0.061 | 0.061 | 0.061 | 0.063 | 0.065 | ||
| Factory \(B\) | 0.031 | 0.056 | 0.049 | 0.044 | 0.038 | 0.048 | 0.051 |
| 0.064 | 0.035 | 0.042 | 0.047 | 0.054 | 0.058 |
| Answer | Marks | Guidance |
|---|---|---|
| Factory A | Factory B | |
| 3 | 1 | 5 8 |
| 9 4 2 | 4 | 7 8 9 |
| 9 8 8 7 4 3 0 | 5 | 1 4 6 8 |
| 5 3 1 | 1 1 | 6 4 |
| M1 | Attempt at ordering | |
| B1 | Factory B | |
| B1 | Correct stem | |
| B1 | Correct leaves Factory A | |
| B1 | Correct leaves Factory B | |
| B1 | Correct key (need Factory A and Factory B and units) | |
| Key: 9 | 4 | 2 represents 0.049 g for Factory A and 0.042 g for Factory B |
| Answer | Marks |
|---|---|
| M1 | Using their key i.e. 48, 0.48, etc. or correct |
**(i)**
Factory A | | Factory B
3 | 1 | 5 8
9 4 2 | 4 | 7 8 9
9 8 8 7 4 3 0 | 5 | 1 4 6 8
5 3 1 | 1 1 | 6 4
M1 | Attempt at ordering
B1 | Factory B
B1 | Correct stem
B1 | Correct leaves Factory A
B1 | Correct leaves Factory B
B1 | Correct key (need Factory A and Factory B and units)
**Key: 9|4|2 represents 0.049 g for Factory A and 0.042 g for Factory B**
[5]
**(ii)**
Median Factory B $= 0.048$ g
M1 | Using their key i.e. 48, 0.48, etc. or correct7 The masses, in grams, of components made in factory $A$ and components made in factory $B$ are shown below.
\begin{center}
\begin{tabular}{ l l l l l l l l }
Factory $A$ & 0.049 & 0.050 & 0.053 & 0.054 & 0.057 & 0.058 & 0.058 \\
& 0.059 & 0.061 & 0.061 & 0.061 & 0.063 & 0.065 & \\
Factory $B$ & 0.031 & 0.056 & 0.049 & 0.044 & 0.038 & 0.048 & 0.051 \\
& 0.064 & 0.035 & 0.042 & 0.047 & 0.054 & 0.058 & \\
\end{tabular}
\end{center}
(i) Draw a back-to-back stem-and-leaf diagram to represent the masses of components made in the two factories.\\
(ii) Find the median and the interquartile range for the masses of components made in factory $B$.\\
(iii) Make two comparisons between the masses of components made in factory $A$ and the masses of those made in factory $B$.
\hfill \mbox{\textit{CAIE S1 2016 Q7 [10]}}