Juniper's Year 1 sample mean, 31.875 days, is a statistic. It is completely determined once the 16 selected observations and the arithmetic convention are fixed. Another valid sample from the same frame would usually produce another mean.
The notation helps keep roles straight: (\bar{x}) commonly labels a sample mean, while (\mu) labels a population mean. The symbols do not create the distinction; the data scope does.
One sample, many statistics
The same observations produce a median, quartiles, range, sample variance, and sample standard deviation. Each statistic answers a different descriptive question and responds differently to the 78-day Year 2 value. A statistic is not “the truth in the sample” in one universal sense.
Some statistics serve as estimators of population parameters. Their usefulness depends on selection design, data quality, assumptions, and the target parameter. A precisely computed statistic from a biased frame remains a fact about that sample, but may be a poor guide to the intended population.
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- Distinguish a statistic computed from the selected observations from the population parameter it may be used to estimate.
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- Sample — Understand
To understand this concept: Required. A statistic is a function of observed sample data.
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- Sampling variability — Understand
Required level here: understand. Required. The quantity that varies across samples is the statistic.
- Statistical inference — Understand
Required level here: understand. Required. Inference begins from a sample-derived quantity.