| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate variance/SD from coded sums |
| Difficulty | Moderate -0.8 This is a straightforward application of standard formulas for variance from coded data. Students need to recall that Var(x) = [Σ(x-c)²]/n - [Σ(x-c)/n]² and that mean = c + [Σ(x-c)]/n. Both parts require direct substitution with minimal algebraic manipulation, making this easier than average for A-level. |
| Spec | 2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(sd^2 = 1957.5/30 - (234/30)^2\) | M1 | Subst in formula or expand |
| \(sd = 2.1\) | A1 [2] | Accept 2.10 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(86 = 234/30 + c\) | M1 | 234/30 seen |
| \(c = 78.2\) | A1 [2] |
## Question 1:
### Part (i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $sd^2 = 1957.5/30 - (234/30)^2$ | M1 | Subst in formula or expand |
| $sd = 2.1$ | A1 **[2]** | Accept 2.10 |
### Part (ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $86 = 234/30 + c$ | M1 | 234/30 seen |
| $c = 78.2$ | A1 **[2]** | |
---1 A summary of 30 values of $x$ gave the following information:
$$\Sigma ( x - c ) = 234 , \quad \Sigma ( x - c ) ^ { 2 } = 1957.5 ,$$
where $c$ is a constant.\\
(i) Find the standard deviation of these values of $x$.\\
(ii) Given that the mean of these values is 86 , find the value of $c$.
\hfill \mbox{\textit{CAIE S1 2013 Q1 [4]}}