| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Interquartile range and percentiles |
| Difficulty | Moderate -0.8 This question tests basic properties of the continuous uniform distribution (median and IQR formulas) which are straightforward to recall and apply, followed by a conceptual critique requiring minimal statistical insight. The calculations are trivial (finding midpoint and quartiles of an interval), and the modeling critique is a standard textbook discussion point about uniform distributions being unrealistic for physical phenomena that tend to cluster around a mean. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf |
| Answer | Marks |
|---|---|
| median = 125 m, IQR = middle half = 25 m (or 137.5 − 112.5) | A1, M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. likely to have higher prob. dens. near median and some values more than 25 m away from median | B2 | (5) |
**Part (a)**
median = 125 m, IQR = middle half = 25 m (or 137.5 − 112.5) | A1, M1 A1 |
**Part (b)**
e.g. likely to have higher prob. dens. near median and some values more than 25 m away from median | B2 | (5)
---A golfer believes that the distance, in metres, that she hits a ball with a 5 iron, follows a continuous uniform distribution over the interval $[100, 150]$.
\begin{enumerate}[label=(\alph*)]
\item Find the median and interquartile range of the distance she hits a ball, that would be predicted by this model. [3 marks]
\item Explain why the continuous uniform distribution may not be a suitable model. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q1 [5]}}