| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Easy -1.2 This is a straightforward data handling question requiring construction of a frequency table from given information and calculation of basic summary statistics (mean and variance). It involves routine application of standard formulas with no conceptual challenges or problem-solving insight required—simpler than the typical A-level question. |
| Spec | 7.02b Graph terminology: tree, simple, connected, simply connected |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(16\) | B1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(8\) | B1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Matches: 1, 2, 3, 4, 5 | M1 | Matches 1,2,3,4,5 |
| Freq: 16, 8, 4, 2, 2 | A1 | 3 correct frequencies |
| A1 | 3 All correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\text{mean} = 62/32 = 1.9375\ (\approx 1.94)\) | M1 | Using their \(\Sigma fx / \Sigma f\) |
| A1 | Correct answer | |
| \(\text{var} = 166/32 - (62/32)^2 = 1.43\) | M1 | Substituting in \(\Sigma fx^2 - (\Sigma fx/n)^2\) formula |
| A1 | 4 Correct answer, or B2 if used calculator |
## Question 6(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $16$ | B1 | **1** |
## Question 6(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $8$ | B1 | **1** |
## Question 6(iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Matches: 1, 2, 3, 4, 5 | M1 | Matches 1,2,3,4,5 |
| Freq: 16, 8, 4, 2, 2 | A1 | 3 correct frequencies |
| | A1 | **3** All correct |
## Question 6(iv):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\text{mean} = 62/32 = 1.9375\ (\approx 1.94)$ | M1 | Using their $\Sigma fx / \Sigma f$ |
| | A1 | Correct answer |
| $\text{var} = 166/32 - (62/32)^2 = 1.43$ | M1 | Substituting in $\Sigma fx^2 - (\Sigma fx/n)^2$ formula |
| | A1 | **4** Correct answer, or B2 if used calculator |
---(i) How many teams play in only 1 match?\\
(ii) How many teams play in exactly 2 matches?\\
(iii) Draw up a frequency table for the numbers of matches which the teams play.\\
(iv) Calculate the mean and variance of the numbers of matches which the teams play.
\hfill \mbox{\textit{CAIE S1 2006 Q6 [9]}}