Easy -1.2 This is a straightforward application of the coding formula for variance. Given Σ(x-a) and Σ(x-a)² with n=20, students apply the standard formulas: variance = Σ(x-a)²/n - [Σ(x-a)/n]² and Σx² = Σ(x-a)² + 2aΣ(x-a) + na². This requires only direct substitution into memorized formulas with no problem-solving or conceptual insight needed, making it easier than average.
2 A summary of the speeds, \(x\) kilometres per hour, of 22 cars passing a certain point gave the following information:
$$\Sigma ( x - 50 ) = 81.4 \text { and } \Sigma ( x - 50 ) ^ { 2 } = 671.0 .$$
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:
$$\Sigma ( x - 50 ) = 81.4 \text { and } \Sigma ( x - 50 ) ^ { 2 } = 671.0 .$$
Find the variance of the speeds and hence find the value of $\Sigma x ^ { 2 }$.\\
\hfill \mbox{\textit{CAIE S1 2020 Q2 [4]}}