| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Standard unbiased estimates calculation |
| Difficulty | Easy -1.3 This is a straightforward S2 question testing basic sampling methods and standard formulas for unbiased estimates. Part (ii) requires direct application of memorized formulas (mean = Σx/n, variance = Σ(x-x̄)²/(n-1)), with no conceptual challenge or problem-solving. Parts (i), (iii), and (iv) test definitional knowledge only. The calculations are routine with small numbers. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc5.05b Unbiased estimates: of population mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Put names in a hat and draw out, or assign a number to each person in year and generate 7 random numbers by calculator. | B1 (1) | Or any equivalent method, could use systematic sampling |
| (ii) est pop mean \(116.5/7 (= 16.6)\) | B1 M1 | For using a correct formula (can be implied) |
| est pop var \(= 27.1\) | A1 (3) | For correct answer |
| (iii) more | B1 (1) | |
| (iv) (pocket money of) all pupils in Jenny's year at school | B1 (1) | Need to see all of this |
**(i)** Put names in a hat and draw out, or assign a number to each person in year and generate 7 random numbers by calculator. | B1 (1) | Or any equivalent method, could use systematic sampling
**(ii)** est pop mean $116.5/7 (= 16.6)$ | B1 M1 | For using a correct formula (can be implied)
est pop var $= 27.1$ | A1 (3) | For correct answer
**(iii)** more | B1 (1) |
**(iv)** (pocket money of) all pupils in Jenny's year at school | B1 (1) | Need to see all of this2 Jenny has to do a statistics project at school on how much pocket money, in dollars, is received by students in her year group. She plans to take a sample of 7 students from her year group, which contains 122 students.\\
(i) Give a suitable method of taking this sample.
Her sample gives the following results.
$$\begin{array} { l l l l l l l }
13.40 & 10.60 & 26.50 & 20.00 & 14.50 & 15.00 & 16.50
\end{array}$$
(ii) Find unbiased estimates of the population mean and variance.\\
(iii) Is the estimated population variance more than, less than or the same as the sample variance?\\
(iv) Describe what you understand by 'population' in this question.
\hfill \mbox{\textit{CAIE S2 2005 Q2 [6]}}