| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Standard unbiased estimates calculation |
| Difficulty | Easy -1.3 This question tests basic statistical definitions and routine calculation of unbiased estimates using standard formulas (mean = Σx/n, variance = Σ(x-x̄)²/(n-1)). Part (i) and (iii) require simple recall of terminology, while part (ii) is straightforward arithmetic with no conceptual challenge—well below average A-level difficulty. |
| Spec | 2.01a Population and sample: terminology5.05b Unbiased estimates: of population mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Each employee has an equal chance of being chosen | B1 [1] | oe |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Est \((\mu) = 4\) | B1 | |
| Est \((\sigma^2) = \frac{10}{9}\left(\frac{199.22}{10} - {`4'}^2\right)\) | M1 | sub in correct formula attempted |
| \(= 4.36\) (3 sf) | A1 [3] | working may not be seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Distances travelled by all employees at the firm | B1 [1] | oe |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Each employee has an equal chance of being chosen | B1 [1] | oe |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Est $(\mu) = 4$ | B1 | |
| Est $(\sigma^2) = \frac{10}{9}\left(\frac{199.22}{10} - {`4'}^2\right)$ | M1 | sub in correct formula attempted |
| $= 4.36$ (3 sf) | A1 [3] | working may not be seen |
### Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Distances travelled by all employees at the firm | B1 [1] | oe |
---2 A researcher is investigating the lengths, in kilometres, of the journeys to work of the employees at a certain firm. She takes a random sample of 10 employees.\\
(i) State what is meant by 'random' in this context.
The results of her sample are as follows.
$$\begin{array} { l l l l l l l l l l }
1.5 & 2.0 & 3.6 & 5.9 & 4.8 & 8.7 & 3.5 & 2.9 & 4.1 & 3.0
\end{array}$$
(ii) Find unbiased estimates of the population mean and variance.\\
(iii) State what is meant by 'population' in this context.
\hfill \mbox{\textit{CAIE S2 2016 Q2 [5]}}