Easy -1.2 This is a straightforward application of the computational formula for variance: Σ(x-x̄)² = Σx² - (Σx)²/n. Requires only direct substitution of given values with minimal calculation steps, making it easier than average A-level questions which typically involve more problem-solving or multi-step reasoning.
1 The ages, \(x\) years, of 150 cars are summarised by \(\Sigma x = 645\) and \(\Sigma x ^ { 2 } = 8287.5\). Find \(\Sigma ( x - \bar { x } ) ^ { 2 }\), where \(\bar { x }\) denotes the mean of \(x\).
$x = 4.3$ | B1 | 4.3 or 645/150 or 18.49 seen
$sd = \sqrt{\left(\frac{8287.5}{150} - 4.3^2\right)} = \sqrt{36.76} = 6.063$ | M1 | Subst in incorrect formula to find sd or var or expand $\Sigma(x - \bar{x})^2$ correctly and substitute
$\Sigma(x - \bar{x})^2 = 150 \times 6.063^2 = 5514$ (5510) | M1 | Mult by 150
| A1 [4] | Answer rounding to 5510
1 The ages, $x$ years, of 150 cars are summarised by $\Sigma x = 645$ and $\Sigma x ^ { 2 } = 8287.5$. Find $\Sigma ( x - \bar { x } ) ^ { 2 }$, where $\bar { x }$ denotes the mean of $x$.
\hfill \mbox{\textit{CAIE S1 2012 Q1 [4]}}