| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | November |
| Marks | 7 |
| 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 -1.8 This is a straightforward data handling question requiring basic statistical skills: organizing data into a stem-and-leaf diagram and calculating median/IQR from ordered data. These are routine procedures with no problem-solving or conceptual challenge, making it significantly easier than average A-level questions. |
| Spec | 2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| sugar | flour | |
| 8 1 | 194 1 5 9 | |
| 7 | 195 3 | |
| 9 4 3 | 196 2 4 | |
| 4 | 197 7 | |
| 8 | 198 | |
| 7 4 1 | 199 | |
| 200 | ||
| 201 | ||
| key: \(1 \mid 196 \mid 2\) means 1.961 kg for sugar and 1.962 kg for flour | B1 | Correct stem must be integers. (stem and leaves can be in reverse order) |
| B1 | Correct leaves flour must be single and ordered | |
| B1 | Correct leaves sugar must be single and ordered | |
| B1ft [4] | Correct key needs all this, ft if single leaves and 1.96 etc in stem |
| Answer | Marks | Guidance |
|---|---|---|
| med \(= 1.989\) kg | B1 | correct median |
| IQ range \(= 2.011 - 1.977\) | M1 | subt their LQ from their UQ, UQ > med, LQ < med |
| \(= 0.034\) kg | A1 [3] | Correct answer |
**(i)**
| sugar | flour |
|-------|-------|
| 8 1 | 194 1 5 9 |
| 7 | 195 3 |
| 9 4 3 | 196 2 4 |
| 4 | 197 7 |
| 8 | 198 |
| 7 4 1 | 199 |
| | 200 |
| | 201 |
key: $1 \mid 196 \mid 2$ means 1.961 kg for sugar and 1.962 kg for flour | B1 | Correct stem must be integers. (stem and leaves can be in reverse order)
| B1 | Correct leaves flour must be single and ordered
| B1 | Correct leaves sugar must be single and ordered
| B1ft [4] | Correct key needs all this, ft if single leaves and 1.96 etc in stem
**(ii)**
med $= 1.989$ kg | B1 | correct median
IQ range $= 2.011 - 1.977$ | M1 | subt their LQ from their UQ, UQ > med, LQ < med
$= 0.034$ kg | A1 [3] | Correct answer4 The weights in kilograms of 11 bags of sugar and 7 bags of flour are as follows.\\
Sugar: 1.9611 .98312 .00812 .0141 .9681 .9941 .2 .0112 .0171 .9771 .9841 .989\\
Flour: $\begin{array} { l l l l l l l } 1.945 & 1.962 & 1.949 & 1.977 & 1.964 & 1.941 & 1.953 \end{array}$\\
(i) Represent this information on a back-to-back stem-and-leaf diagram with sugar on the left-hand side.\\
(ii) Find the median and interquartile range of the weights of the bags of sugar.
\hfill \mbox{\textit{CAIE S1 2010 Q4 [7]}}