| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate variance from summary statistics |
| Difficulty | Easy -1.2 This is a straightforward application of standard formulas for mean and standard deviation from summary statistics (Σx and Σx²). Part (i) requires direct substitution into memorized formulas with simple arithmetic, while part (ii) asks for basic interpretation of two numbers. No problem-solving or conceptual insight needed—purely routine calculation and description. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| Mean is 84.8 minutes | B1 | For correct value 84.8 |
| Standard deviation = \(\sqrt{\frac{180044}{25} - 84.8^2} = 3.27\) minutes | M1 | For correct formula or calculator use |
| A1 | For correct value 3.27 |
| Answer | Marks | Guidance |
|---|---|---|
| John's average time is about 5 minutes less than Janet's. John's times are more variable than Janet's | B1√ | For correct comparison of averages |
| B1√ | For correct comparison of variability |
**Part (i)**
Mean is 84.8 minutes | B1 | For correct value 84.8
Standard deviation = $\sqrt{\frac{180044}{25} - 84.8^2} = 3.27$ minutes | M1 | For correct formula or calculator use
| A1 | For correct value 3.27
**Part (ii)**
John's average time is about 5 minutes less than Janet's. John's times are more variable than Janet's | B1√ | For correct comparison of averages
| B1√ | For correct comparison of variability
---1 Janet and John wanted to compare their daily journey times to work, so they each kept a record of their journey times for a few weeks.\\
(i) Janet's daily journey times, $x$ minutes, for a period of 25 days, were summarised by $\Sigma x = 2120$ and $\Sigma x ^ { 2 } = 180044$. Calculate the mean and standard deviation of Janet's journey times.\\
(ii) John's journey times had a mean of 79.7 minutes and a standard deviation of 6.22 minutes. Describe briefly, in everyday terms, how Janet and John's journey times compare.
\hfill \mbox{\textit{OCR S1 Q1 [5]}}