| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | 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 for mean and standard deviation, followed by routine linear transformations (y = 500 + 100x). Part (iii) requires only basic interpretation of transformed statistics. All steps are mechanical with no problem-solving or novel insight required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation5.02c Linear coding: effects on mean and variance |
2 Dwayne is a car salesman. The numbers of cars, $x$, sold by Dwayne each month during the year 2008 are summarised by
$$n = 12 , \quad \Sigma x = 126 , \quad \Sigma x ^ { 2 } = 1582 .$$
(i) Calculate the mean and standard deviation of the monthly numbers of cars sold.\\
(ii) Dwayne earns $\pounds 500$ each month plus $\pounds 100$ commission for each car sold. Show that the mean of Dwayne's monthly earnings is $\pounds 1550$. Find the standard deviation of Dwayne's monthly earnings.\\
(iii) Marlene is a car saleswoman and is paid in the same way as Dwayne. During 2008 her monthly earnings have mean $\pounds 1625$ and standard deviation $\pounds 280$. Briefly compare the monthly numbers of cars sold by Marlene and Dwayne during 2008.
\hfill \mbox{\textit{OCR MEI S1 Q2 [8]}}