Easy -1.2 This is a straightforward application of standard formulas for unbiased estimates of mean (Σx/n) and variance (Σx²/(n-1) - n(x̄)²/(n-1)). It requires only direct substitution into memorized formulas with no problem-solving, conceptual understanding, or multi-step reasoning—purely mechanical calculation that is easier than average A-level questions.
1 A random sample of 100 values of a variable \(X\) is taken. These values are summarised below.
$$n = 100 \quad \Sigma x = 1556 \quad \Sigma x ^ { 2 } = 29004$$
Calculate unbiased estimates of the population mean and variance of \(X\).
1 A random sample of 100 values of a variable $X$ is taken. These values are summarised below.
$$n = 100 \quad \Sigma x = 1556 \quad \Sigma x ^ { 2 } = 29004$$
Calculate unbiased estimates of the population mean and variance of $X$.\\
\hfill \mbox{\textit{CAIE S2 2020 Q1 [3]}}