| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Forward transformation: find new statistics |
| Difficulty | Moderate -0.8 This is a straightforward application of standard formulas and transformation rules. Part (i) requires direct substitution into mean and standard deviation formulas. Parts (ii) and (iii) test knowledge of how linear transformations affect statistics (multiplication affects both mean and SD; addition affects only mean). All steps are routine with no problem-solving or conceptual challenges beyond basic recall. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
2 The hourly wages, $\pounds x$, of a random sample of 60 employees working for a company are summarised as follows.
$$n = 60 \quad \sum x = 759.00 \quad \sum x ^ { 2 } = 11736.59$$
(i) Calculate the mean and standard deviation of $x$.\\
(ii) The workers are offered a wage increase of $2 \%$. Use your answers to part (i) to deduce the new mean and standard deviation of the hourly wages after this increase.\\
(iii) As an alternative the workers are offered a wage increase of 25 p per hour. Write down the new mean and standard deviation of the hourly wages after this 25p increase.
\hfill \mbox{\textit{OCR MEI S1 2012 Q2 [7]}}