Moderate -0.8 This is a straightforward application of the variance formula requiring algebraic manipulation. Students must recall the unbiased variance formula, set up an equation with the unknown 'a', and solve a quadratic. While it involves multiple steps, it's a standard textbook exercise with no conceptual difficulty or novel insight required—easier than average A-level questions.
6 A sample of 5 randomly selected values of a variable \(X\) is as follows:
$$\begin{array} { l l l l l }
1 & 2 & 6 & 1 & a
\end{array}$$
where \(a > 0\).
Given that an unbiased estimate of the variance of \(X\) calculated from this sample is \(\frac { 11 } { 2 }\), find the value of \(a\).
6 A sample of 5 randomly selected values of a variable $X$ is as follows:
$$\begin{array} { l l l l l }
1 & 2 & 6 & 1 & a
\end{array}$$
where $a > 0$.\\
Given that an unbiased estimate of the variance of $X$ calculated from this sample is $\frac { 11 } { 2 }$, find the value of $a$.\\
\hfill \mbox{\textit{CAIE S2 2023 Q6 [3]}}