| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Sampling frames and populations |
| Difficulty | Easy -1.8 This is a pure definitional question requiring only recall of basic statistical terminology (population, statistic, sampling distribution) with no calculations or problem-solving. The application in parts (c)-(d) is straightforward identification from a given context. This is significantly easier than average A-level questions which typically require multi-step calculations or conceptual application. |
| Spec | 2.01a Population and sample: terminology5.05a Sample mean distribution: central limit theorem |
| Answer | Marks | Guidance |
|---|---|---|
| (a) A population is a collection of all items | B1 (1) | — |
| (b) (A random variable) that is a function of the sample which contains no unknown quantities/parameters. | B1 (1) | Solely/only imply no unknown quantities. Do not allow unknown variables e.g. "A calculation based solely on observations from a given sample." B1, "A calculation based only on known data from a sample" B1, "A calculation based on known observations from a sample" B0 |
| (c) The voters in the town | B1 (2) | Do not allow 100 voters. |
| Percentage/proportion voting for Dr Smith | B1 | the number of people voting (for Dr Smith): Allow 35% of people voting (for Dr Smith); Allow 35 people voting (for Dr Smith); Do not allow 35% or 35 alone |
| (d) Probability Distribution of those voting for Dr Smith from all possible samples (of size 100) | B1 (1) | Answers must include all three of these features: (i) All possible samples, (ii) their associated probabilities, (iii) context of voting for Dr Smith. e.g "It is all possible values of the percentage and their associated probabilities." B0 no context |
**(a)** A population is a collection of all items | B1 (1) | —
**(b)** (A random variable) that is a function of the sample which contains no unknown quantities/parameters. | B1 (1) | Solely/only imply no unknown quantities. Do not allow unknown variables e.g. "A calculation based solely on observations from a given sample." B1, "A calculation based only on known data from a sample" B1, "A calculation based on known observations from a sample" B0
**(c)** The voters in the town | B1 (2) | Do not allow 100 voters.
Percentage/proportion voting for Dr Smith | B1 | the number of people voting (for Dr Smith): Allow 35% of people voting (for Dr Smith); Allow 35 people voting (for Dr Smith); Do not allow 35% or 35 alone
**(d)** Probability Distribution of those voting for Dr Smith from all possible samples (of size 100) | B1 (1) | Answers must include all three of these features: (i) All possible samples, (ii) their associated probabilities, (iii) context of voting for Dr Smith. e.g "It is all possible values of the percentage and their associated probabilities." B0 no context
---Explain what you understand by
\begin{enumerate}[label=(\alph*)]
\item a population, [1]
\item a statistic. [1]
\end{enumerate}
A researcher took a sample of 100 voters from a certain town and asked them who they would vote for in an election. The proportion who said they would vote for Dr Smith was 35\%.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item State the population and the statistic in this case. [2]
\item Explain what you understand by the sampling distribution of this statistic. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2010 Q1 [5]}}