| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Combined with coded data |
| Difficulty | Standard +0.3 This is a standard coded data question requiring application of formulas for combining datasets. Students must decode the summations to find the combined mean and standard deviation using well-practiced techniques (Σx = Σ(x-30) + 30n, then apply variance formula). It's slightly above average difficulty due to the two-dataset combination and algebraic manipulation required, but follows a predictable pattern commonly taught in S1. |
| Spec | 2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\text{Mean} = \frac{439+470}{45}+30\) | M1 | \(\frac{439+470}{45}\) or \(\frac{909}{45}\) seen |
| \(= 50.2\) | A1 | If M0 awarded, SC B1 50.2 WWW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\text{Mean} = \frac{25\times30+470+20\times30+439}{45}\) | (M1) | \(\frac{1220+1039}{45}\) or \(\frac{2259}{45}\) seen |
| \(= 50.2\) | (A1) | If M0 awarded, SC B1 50.2 WWW |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\text{Sd}^2 = \frac{12405+11346}{45} - \left(\frac{909}{45}\right)^2\) | M1 | \(\frac{\text{their}(12405+11346)}{45}\) or \(23751 - \left(\text{their}\frac{909}{45}\right)^2\) |
| \(\text{sd} = \sqrt{119.76} = 10.9\) | A1 | If M0 awarded, SC B1 10.9 WWW |
## Question 1:
**Part (a):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{Mean} = \frac{439+470}{45}+30$ | M1 | $\frac{439+470}{45}$ or $\frac{909}{45}$ seen |
| $= 50.2$ | A1 | If M0 awarded, SC B1 50.2 WWW |
*Alternative Method:*
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{Mean} = \frac{25\times30+470+20\times30+439}{45}$ | (M1) | $\frac{1220+1039}{45}$ or $\frac{2259}{45}$ seen |
| $= 50.2$ | (A1) | If M0 awarded, SC B1 50.2 WWW |
**Total: 2 marks**
**Part (b):**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{Sd}^2 = \frac{12405+11346}{45} - \left(\frac{909}{45}\right)^2$ | M1 | $\frac{\text{their}(12405+11346)}{45}$ or $23751 - \left(\text{their}\frac{909}{45}\right)^2$ |
| $\text{sd} = \sqrt{119.76} = 10.9$ | A1 | If M0 awarded, SC B1 10.9 WWW |
**Total: 2 marks**
---1 A summary of 20 values of $x$ gives
$$\Sigma ( x - 30 ) = 439 , \quad \Sigma ( x - 30 ) ^ { 2 } = 12405 .$$
A summary of another 25 values of $x$ gives
$$\sum ( x - 30 ) = 470 , \quad \sum ( x - 30 ) ^ { 2 } = 11346 .$$
\begin{enumerate}[label=(\alph*)]
\item Find the mean of all 45 values of $x$.
\item Find the standard deviation of all 45 values of $x$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2024 Q1 [4]}}