| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | June |
| 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 -1.8 This is a routine data handling exercise requiring only mechanical application of standard procedures: constructing a stem-and-leaf diagram from ordered data, finding median/quartiles by position (n=27 makes this straightforward), and applying the given outlier formula. No problem-solving or statistical insight required—purely procedural recall. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02h Recognize outliers |
| 10 | 40 | 60 | 80 | 100 | 130 | 140 | 140 | 140 |
| 150 | 150 | 150 | 160 | 160 | 160 | 160 | 170 | 180 |
| 180 | 200 | 210 | 250 | 270 | 280 | 310 | 450 | 570 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Stem\ | Leaf diagram: \(0 \mid 1\ 4\ 6\ 8\); \(1 \mid 0\ 3\ 4\ 4\ 4\ 5\ 5\ 5\ 6\ 6\ 6\ 6\ 7\ 8\ 8\); \(2 \mid 0\ 1\ 5\ 7\ 8\); \(3 \mid 1\); \(4 \mid 5\); \(5 \mid 7\) | B1 |
| Correct leaves | B1 | Correct leaves must be single digits and one line for each stem value or 2 lines each stem value |
| Key \(1 \mid 4\) represents \\(140 | B1ft [3] | Correct key must have \\), ft 2 special cases |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Median \(= 160\); \(LQ = 140\), \(UQ = 210\) | B1 | |
| \(IQ\ \text{range} = UQ - LQ\) | M1 | Subtract their LQ from their UQ |
| \(= 70\) | A1 [3] | Correct answer cwo |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1.5 \times IQ\ \text{range} = 105\) | M1 | Multiply their IQ range by 1.5 (can be implied) |
| Lower outlier is below \(35\); Upper outlier is above \(315\) | A1ft | Correct limits ft their IQ range and quartiles |
| Outliers: \(10, 450, 570\) | A1 [3] | Correct outliers |
## Question 5:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Stem\|Leaf diagram: $0 \mid 1\ 4\ 6\ 8$; $1 \mid 0\ 3\ 4\ 4\ 4\ 5\ 5\ 5\ 6\ 6\ 6\ 6\ 7\ 8\ 8$; $2 \mid 0\ 1\ 5\ 7\ 8$; $3 \mid 1$; $4 \mid 5$; $5 \mid 7$ | B1 | Correct stem, condone a space under the 1 |
| Correct leaves | B1 | Correct leaves must be single digits and one line for each stem value or 2 lines each stem value |
| Key $1 \mid 4$ represents \$140 | B1ft **[3]** | Correct key must have \$, ft 2 special cases |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Median $= 160$; $LQ = 140$, $UQ = 210$ | B1 | |
| $IQ\ \text{range} = UQ - LQ$ | M1 | Subtract their LQ from their UQ |
| $= 70$ | A1 **[3]** | Correct answer cwo |
### Part (iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1.5 \times IQ\ \text{range} = 105$ | M1 | Multiply their IQ range by 1.5 (can be implied) |
| Lower outlier is below $35$; Upper outlier is above $315$ | A1ft | Correct limits ft their IQ range and quartiles |
| Outliers: $10, 450, 570$ | A1 **[3]** | Correct outliers |
---5 The following are the annual amounts of money spent on clothes, to the nearest $\$ 10$, by 27 people.
\begin{center}
\begin{tabular}{ r r r r r r r r r }
10 & 40 & 60 & 80 & 100 & 130 & 140 & 140 & 140 \\
150 & 150 & 150 & 160 & 160 & 160 & 160 & 170 & 180 \\
180 & 200 & 210 & 250 & 270 & 280 & 310 & 450 & 570 \\
\end{tabular}
\end{center}
(i) Construct a stem-and-leaf diagram for the data.\\
(ii) Find the median and the interquartile range of the data.
An 'outlier' is defined as any data value which is more than 1.5 times the interquartile range above the upper quartile, or more than 1.5 times the interquartile range below the lower quartile.\\
(iii) List the outliers.
\hfill \mbox{\textit{CAIE S1 2013 Q5 [9]}}