| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate range and interquartile range |
| Difficulty | Easy -1.8 This question requires only direct reading of values from a box plot (range and IQR), applying a standard outlier formula (1.5×IQR rule), and basic description of skewness. All three parts involve straightforward recall and minimal calculation with no problem-solving or conceptual depth required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02h Recognize outliers |
| Answer | Marks | Guidance |
|---|---|---|
| Range \(= 55 - 15 = 40\) | B1 | cao |
| IQR \(= 35 - 26 = 9\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| \(Q_3 + 1.5 \times IQR = 35 + 13.5 = 48.5\) | M1 | Correct method for either fence |
| \(Q_1 - 1.5 \times IQR = 26 - 13.5 = 12.5\) | ||
| 55 is an outlier (since \(55 > 48.5\)), 15 is not an outlier (since \(15 > 12.5\)) | A1 A1 |
| Answer | Marks |
|---|---|
| Positively skewed | B1 |
# Question 1:
**(i)**
Range $= 55 - 15 = 40$ | B1 | cao
IQR $= 35 - 26 = 9$ | B1 | cao
**(ii)**
$Q_3 + 1.5 \times IQR = 35 + 13.5 = 48.5$ | M1 | Correct method for either fence
$Q_1 - 1.5 \times IQR = 26 - 13.5 = 12.5$ | |
55 is an outlier (since $55 > 48.5$), 15 is not an outlier (since $15 > 12.5$) | A1 A1 |
**(iii)**
Positively skewed | B1 |
---1 The times taken, in minutes, by 80 people to complete a crossword puzzle are summarised by the box and whisker plot below.\\
\includegraphics[max width=\textwidth, alt={}, center]{acb05873-e441-4b95-9732-6ebd5ae79fa6-2_147_848_507_612}\\
(i) Write down the range and the interquartile range of the times.\\
(ii) Determine whether any of the times can be regarded as outliers.\\
(iii) Describe the shape of the distribution of the times.
\hfill \mbox{\textit{OCR MEI S1 2006 Q1 [6]}}