| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | November |
| Marks | 5 |
| 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 to calculate mean and variance. It requires only routine arithmetic with given data values, substitution into standard formulas, and basic algebraic manipulation. The coding method (subtracting 62) is explicitly guided by the question structure, making this easier than average A-level work. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(0.7 - 2.4 + 2.2 - 0.5 + 6.3 + 4.9 + 0 + 0.3 = 11.5\) | B1 1 | |
| (ii) \((0.7^2 + 2.4^2 + 2.2^2 + 0.5^2 + 6.3^2 + 4.9^2 + 0.3^2) = 75.13\) (75.1) | B1 1 | |
| (iii) mean \(= 63.4375\) | B1√ | ft 62 + their (i)/8 |
| Variance \(= 75.13/8 - (11.5/8)^2 = 7.32\) | M1 | their(i)/8 \(-\) ((i)/8)\(^2\) |
| A1 3 | correct answer | |
| OR mean \(= 507.5/8 = 63.4375\) | B1 | |
| Var \(= 32253/8 - 63.4375^2 = 7.32\) | M1 | subst in correct variance or standard deviation formula |
| A1 | correct answer – allow 6.62, 6.93–7.04, 7.260–7.325 | |
| Marks can be awarded in (i) or (ii) if not 'contradicted' by further working |
**(i)** $0.7 - 2.4 + 2.2 - 0.5 + 6.3 + 4.9 + 0 + 0.3 = 11.5$ | B1 1 |
**(ii)** $(0.7^2 + 2.4^2 + 2.2^2 + 0.5^2 + 6.3^2 + 4.9^2 + 0.3^2) = 75.13$ (75.1) | B1 1 |
**(iii)** mean $= 63.4375$ | B1√ | ft 62 + their (i)/8
Variance $= 75.13/8 - (11.5/8)^2 = 7.32$ | M1 | their(i)/8 $-$ ((i)/8)$^2$
| A1 3 | correct answer
OR mean $= 507.5/8 = 63.4375$ | B1 |
Var $= 32253/8 - 63.4375^2 = 7.32$ | M1 | subst in correct variance or standard deviation formula
| A1 | correct answer – allow 6.62, 6.93–7.04, 7.260–7.325
| | Marks can be awarded in (i) or (ii) if not 'contradicted' by further working2 A traffic camera measured the speeds, $x$ kilometres per hour, of 8 cars travelling along a certain street, with the following results.
$$\begin{array} { l l l l l l l l }
62.7 & 59.6 & 64.2 & 61.5 & 68.3 & 66.9 & 62.0 & 62.3
\end{array}$$
(i) Find $\Sigma ( x - 62 )$.\\
(ii) Find $\Sigma ( x - 62 ) ^ { 2 }$.\\
(iii) Find the mean and variance of the speeds of the 8 cars.
\hfill \mbox{\textit{CAIE S1 2014 Q2 [5]}}