| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| 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 straightforward question testing basic understanding of sampling bias and routine calculation of mean and variance from a small dataset. Part (i) and (ii) require simple conceptual reasoning about representativeness, while part (iii) involves direct application of standard formulas with no algebraic manipulation or problem-solving required. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | B1 [1] | Commuters are not representative of the whole population |
| (ii) | B1 [1] | People who travel to work on (this) train |
| (iii) | Mean = 6.17 o.e. | B1 |
| Variance = \(\frac{1}{11}\left(463.56 - \frac{74^2}{12}\right) = 0.657\) | M1 | Substituting in formula from tables |
| A1 [3] | Correct answer |
(i) | B1 [1] | Commuters are not representative of the whole population
(ii) | B1 [1] | People who travel to work on (this) train | Any sensible answer
(iii) | Mean = 6.17 o.e. | B1 |
Variance = $\frac{1}{11}\left(463.56 - \frac{74^2}{12}\right) = 0.657$ | M1 | Substituting in formula from tables
| | A1 [3] | Correct answer
---1 A magazine conducted a survey about the sleeping time of adults. A random sample of 12 adults was chosen from the adults travelling to work on a train.\\
(i) Give a reason why this is an unsatisfactory sample for the purposes of the survey.\\
(ii) State a population for which this sample would be satisfactory.
A satisfactory sample of 12 adults gave numbers of hours of sleep as shown below.\\
$4.6 \quad 6.8$\\
5.2\\
6.2\\
5.7\\
$\begin{array} { l l } 7.1 & 6.3 \end{array}$\\
5.6\\
7.0\\
$5.8 \quad 6.5$\\
7.2\\
(iii) Calculate unbiased estimates of the mean and variance of the sleeping times of adults.
\hfill \mbox{\textit{CAIE S2 2008 Q1 [5]}}