Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

A random sample made up of 5 observations of a variable $X$ is shown here: $2,\ 3,\ 3,\ 5,\ a$.
(a)[1]

Find an expression, in terms of $a$, for the mean of this set of values.

(b)[3]

It is stated that the unbiased estimate of the population variance of $X$ from these values is $4$. Also, $a$ is positive. Form and simplify a quadratic equation in terms of $a$, then determine the value of $a$.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct mean is $\frac{13+a}{5}$

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