| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Total sample size from histogram |
| Difficulty | Moderate -0.8 This is a straightforward histogram interpretation question requiring basic skills: reading frequency density from a histogram, calculating frequencies using area = frequency density × class width, and computing a simple conditional probability. All steps are routine with no problem-solving insight needed, making it easier than average A-level work. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02b Histogram: area represents frequency2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(30\)–\(35\) years | B1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(4.8 \times 5 = 24\) | M1 | Multiplying by 5 |
| A1 | 2 Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(4+18+24+28+26+10 = 110\) | M1 | Summing their 6 attempts at frequencies |
| A1 | 2 Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(24/88 = 0.273\) | M1 | Dividing their (ii) by their attempt at \(>25\) group |
| A1ft | 2 Correct answer, ft on above |
## Question 5(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $30$–$35$ years | B1 | **1** |
## Question 5(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $4.8 \times 5 = 24$ | M1 | Multiplying by 5 |
| | A1 | **2** Correct answer |
## Question 5(iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $4+18+24+28+26+10 = 110$ | M1 | Summing their 6 attempts at frequencies |
| | A1 | **2** Correct answer |
## Question 5(iv):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $24/88 = 0.273$ | M1 | Dividing their (ii) by their attempt at $>25$ group |
| | A1ft | **2** Correct answer, ft on above |
---5 Each father in a random sample of fathers was asked how old he was when his first child was born. The following histogram represents the information.\\
\includegraphics[max width=\textwidth, alt={}, center]{14e8a601-2180-4491-9336-cafd262f2596-3_789_1627_1468_260}\\
(i) What is the modal age group?\\
(ii) How many fathers were between 25 and 30 years old when their first child was born?\\
(iii) How many fathers were in the sample?\\
(iv) Find the probability that a father, chosen at random from the group, was between 25 and 30 years old when his first child was born, given that he was older than 25 years.
632 teams enter for a knockout competition, in which each match results in one team winning and the other team losing. After each match the winning team goes on to the next round, and the losing team takes no further part in the competition. Thus 16 teams play in the second round, 8 teams play in the third round, and so on, until 2 teams play in the final round.\\
\hfill \mbox{\textit{CAIE S1 2006 Q5 [7]}}