| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate mean from coded sums |
| Difficulty | Easy -1.2 This is a straightforward application of coding formulas for mean and variance. Part (i) requires simple rearrangement of Σ(x-130)/n = x̄-130, and part (ii) uses the standard variance formula Σ(x-130)²/n = σ². Both are direct recall of standard results with minimal algebraic manipulation, making this easier than average. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\bar{x} = 130 - \frac{287}{82} = 126.5 \text{ (126, 127) cm}\) | M1 | \(\frac{287}{82}\) seen added or subt to 130 OR 287 seen added or subt to \(82 \times 130\) |
| A1 | Correct answer | |
| (ii) \(\frac{\Sigma(x-130)^2}{82} - (-3.5^2) = 6.9^2\) | M1 | \(6.9^2 + (\text{their coded mean})^2\) seen or implied |
| \(\Sigma(x-130)^2 = 4908.5 \text{ cm (4910)}\) | A1 | Correct answer |
**(i)** $\bar{x} = 130 - \frac{287}{82} = 126.5 \text{ (126, 127) cm}$ | M1 | $\frac{287}{82}$ seen added or subt to 130 OR 287 seen added or subt to $82 \times 130$ |
| A1 | Correct answer |
**(ii)** $\frac{\Sigma(x-130)^2}{82} - (-3.5^2) = 6.9^2$ | M1 | $6.9^2 + (\text{their coded mean})^2$ seen or implied |
$\Sigma(x-130)^2 = 4908.5 \text{ cm (4910)}$ | A1 | Correct answer |
---2 The heights, $x \mathrm {~cm}$, of a group of 82 children are summarised as follows.
$$\Sigma ( x - 130 ) = - 287 , \quad \text { standard deviation of } x = 6.9 .$$
(i) Find the mean height.\\
(ii) Find $\Sigma ( x - 130 ) ^ { 2 }$.
\hfill \mbox{\textit{CAIE S1 2010 Q2 [4]}}