| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| 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 straightforward recall question testing definitions of basic statistical terminology (census, sampling frame, sampling unit, statistic). No calculations or problem-solving required—students simply need to state learned definitions. Significantly easier than typical A-level questions which require application of techniques. |
| Spec | 2.01a Population and sample: terminology2.01b Informal inferences: from samples2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| (a) e.g. Population is small | B1 | Any correct characteristic of the population that makes a census a practical alternative to a sample (accessible, finite, well-defined) |
| (b)(i) list/register/database of all members (of the leisure centre) | B1 | B1 idea of list (oe) and idea of all members (e.g. list of each member of the leisure centre) |
| (b)(ii) A member (of the leisure centre) | B1 | B1 a single member. Condone members. Also condone One of the members in the sample. The opinion/view of one of the members is B0 |
| (c) \(C\) is the statistic as it is (a quantity) based only on values (oe) taken from the sample/it contains no unknown parameters/population values | B1 | B1 choosing \(C\) (or clearly identifying \(C\) in words) only with a correct supporting reason which must include value (oe) and sample or no unknown parameters. For values allow e.g. information, observations, calculations, function, numerical data, etc. |
**(a)** e.g. Population is small | B1 | Any correct characteristic of the population that makes a census a practical alternative to a sample (accessible, finite, well-defined)
**(b)(i)** list/register/database of all members (of the leisure centre) | B1 | B1 idea of list (oe) and idea of all members (e.g. list of each member of the leisure centre)
**(b)(ii)** A member (of the leisure centre) | B1 | B1 a single member. Condone members. Also condone One of the members in the sample. The opinion/view of one of the members is B0
**(c)** $C$ is the statistic as it is (a quantity) based only on values (oe) taken from the sample/it contains no unknown parameters/population values | B1 | B1 choosing $C$ (or clearly identifying $C$ in words) only with a correct supporting reason which must include value (oe) and sample or no unknown parameters. For values allow e.g. information, observations, calculations, function, numerical data, etc.\begin{enumerate}
\item (a) State one characteristic of a population that would make a census a practical alternative to sampling.
\end{enumerate}
A leisure centre has 2500 members.\\
It asks a sample of 300 members for their opinions on the fees it charges for using the centre.
For the sample,\\
(b) (i) identify a suitable sampling frame,\\
(ii) identify a sampling unit.
The leisure centre has the following pieces of information.\\
$A$ is the list of the different types of membership that can be paid for by members.\\
$B$ is the mean of the membership fees paid by all 2500 members.\\
$C$ is the number in the sample of 300 members who are satisfied with the fees they pay.\\
(c) State the piece of information that is a statistic.
Give a reason for your answer.
\hfill \mbox{\textit{Edexcel S2 2023 Q2 [4]}}