| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2007 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Random Variables |
| Type | Statistics vs non-statistics identification |
| Difficulty | Easy -1.8 This is a pure definitional recall question requiring students to state the definition of a statistic and identify whether expressions contain unknown population parameters. No calculation, problem-solving, or conceptual application is needed—just memorization and direct application of the definition that a statistic cannot contain unknown parameters like μ. |
| Spec | 5.05b Unbiased estimates: of population mean and variance |
| Answer | Marks |
|---|---|
| A random variable; function of known observations (from a population). data OK | B1M1 (2 marks) |
| Answer | Marks |
|---|---|
| Yes | B1 (1 mark) |
| Answer | Marks |
|---|---|
| No | B1 (1 mark) |
**Part (a)**
A random variable; function of known observations (from a population). data OK | B1M1 (2 marks) |
**Part (b)(i)**
Yes | B1 (1 mark) |
**Part (b)(ii)**
No | B1 (1 mark) |
---\begin{enumerate}
\item (a) Define a statistic.
\end{enumerate}
A random sample $X _ { 1 } , X _ { 2 } , \ldots , X _ { \mathrm { n } }$ is taken from a population with unknown mean $\mu$.\\
(b) For each of the following state whether or not it is a statistic.\\
(i) $\frac { X _ { 1 } + X _ { 4 } } { 2 }$,\\
(ii) $\frac { \sum X ^ { 2 } } { n } - \mu ^ { 2 }$.\\
\hfill \mbox{\textit{Edexcel S2 2007 Q1 [4]}}