Estimating from a sample

Japanese school year: Junior high 3

What you learn

You will learn how to estimate population parameters from sample statistics using proportions and proportional reasoning. This technique is widely applied to estimate wildlife populations and product defect rates. Familiarity with solving ratios and proportional equations will make these concepts much easier to understand.

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Key points

This proportion shows that the ratio in a sample approximately mirrors that of the whole population. The population proportion $\frac{A}{N}$ is roughly equal to the sample proportion $\frac{a}{n}$ .

\frac{a}{n} = \frac{A}{N}

Use this formula to estimate the total count $A$ of items meeting a condition in the population. Multiply the total population size $N$ by the sample proportion $\frac{a}{n}$ .

A \approx N \times \frac{a}{n}

Use this formula to estimate an unknown population size $N$ that cannot be directly counted (the mark-recapture method). It estimates $N$ from the initially marked count $M$ , a recaptured sample size $n$ , and the number of marked individuals found $m$ .

N \approx \frac{M n}{m}

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Practice 1Coming soon