| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Box plot construction or interpretation |
| Difficulty | Easy -1.3 This is a straightforward box plot interpretation question requiring only direct reading of values (range, IQR), application of the standard outlier formula (1.5×IQR), and basic description of skewness. All parts involve routine recall and simple arithmetic with no problem-solving or novel insight required. |
| Spec | 2.02f Measures of average and spread2.02h Recognize outliers |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Range \(= 55 - 15 = 40\) | B1 CAO | |
| Interquartile range \(= 35 - 26 = 9\) | B1 CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(35 + 1.5 \times 9 = 48.5\) | M1 | for 48.5 oe |
| \(26 - 1.5 \times 9 = 12.5\) | M1 | for 12.5 oe |
| Any value \(> 48.5\) is an outlier (so 55 will be an outlier) | A1 | FT their IQR in (i) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| One valid comment e.g. positively skewed OR middle 50% of data is closely bunched | E1 |
## Question 2:
**(i)**
| Answer | Mark | Guidance |
|--------|------|----------|
| Range $= 55 - 15 = 40$ | B1 CAO | |
| Interquartile range $= 35 - 26 = 9$ | B1 CAO | |
**(ii)**
| Answer | Mark | Guidance |
|--------|------|----------|
| $35 + 1.5 \times 9 = 48.5$ | M1 | for 48.5 oe |
| $26 - 1.5 \times 9 = 12.5$ | M1 | for 12.5 oe |
| Any value $> 48.5$ is an outlier (so 55 will be an outlier) | A1 | FT their IQR in (i) |
**(iii)**
| Answer | Mark | Guidance |
|--------|------|----------|
| One valid comment e.g. positively skewed OR middle 50% of data is closely bunched | E1 | |
---2 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]{088972e9-bfcd-429c-9145-af274a4c0a58-2_163_857_436_642}\\
(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 Q2 [6]}}