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Determine the value of $a$.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
A set of $5$ values of the variable $X$, chosen at random, is $1,\ 2,\ 6,\ 1,\ a$, where $a > 0$. If the unbiased estimate of the variance of $X$ found from this sample is $\frac{11}{2}$, determine the value of $a$.
Worked solution & mark scheme
This 3-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write an equation for the unbiased variance, for example $\frac14\left(\frac{42+a^2}{5}-\left(\frac{10+a^2}{5}\right)^2\right)=\frac{11}{2}$.” …
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