Pearson Edexcel IAL Mathematics S2.4.2 Concepts of a statistic & its sampling distribution

Practise defining statistics and sampling distributions, then building distributions for sample-based measures such as the range.

Exam points

explain why an expression involving an unknown population parameter is not a statistic
list possible statistic values and assign probabilities to form a sampling distribution
calculate probabilities for a sample range using combinations of outcomes

[Maximum number: 1]

A random sample of two observations $X_{1}$ and $X_{2}$ is taken from a population with unknown mean $\mu$ and unknown variance $\sigma^{2}$

Explain why $\frac{X_{1}-\mu}{\sigma}$ is not a statistic.

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