Moderate -0.8 This is a straightforward application of standard variance formulas using coded data. Students need to recall the formula for variance from coded sums (Var(x) = Σ(x-a)²/n - [Σ(x-a)/n]²) and then use Σx² = Σ(x-50)² + 100Σ(x-50) + 2500n. Both are direct formula applications with no problem-solving or conceptual insight required, making this easier than average.
2 A summary of the speeds, \(x\) kilometres per hour, of 22 cars passing a certain point gave the following information:
$$\Sigma ( x - 50 ) = 81.4 \quad \text { and } \quad \Sigma ( x - 50 ) ^ { 2 } = 671.0 .$$
Find the variance of the speeds and hence find the value of \(\Sigma x ^ { 2 }\).
2 A summary of the speeds, $x$ kilometres per hour, of 22 cars passing a certain point gave the following information:
$$\Sigma ( x - 50 ) = 81.4 \quad \text { and } \quad \Sigma ( x - 50 ) ^ { 2 } = 671.0 .$$
Find the variance of the speeds and hence find the value of $\Sigma x ^ { 2 }$.
\hfill \mbox{\textit{CAIE S1 2013 Q2 [4]}}