Easy -1.2 This is a straightforward application of standard formulas for unbiased estimates of mean (x̄ = Σx/n) and variance (s² = [Σx² - (Σx)²/n]/(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 a typical A-level question.
1 A random sample of 75 values of a variable \(X\) gave the following results.
$$n = 75 \quad \Sigma x = 153.2 \quad \Sigma x ^ { 2 } = 340.24$$
Find unbiased estimates for the population mean and variance of \(X\).
1 A random sample of 75 values of a variable $X$ gave the following results.
$$n = 75 \quad \Sigma x = 153.2 \quad \Sigma x ^ { 2 } = 340.24$$
Find unbiased estimates for the population mean and variance of $X$.\\
\hfill \mbox{\textit{CAIE S2 2018 Q1 [3]}}