Statistics & Probability
GradesGrade 7Statistics & ProbabilityRandom Sampling & Inference

Random Sampling & Inference

🎲 Statistics & Probability
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Random Sampling & Inference

A random sample represents the whole population — use it to make valid predictions.

A population is the entire group you want to study. Since studying every member is often impractical, we take a sample. A random sample gives every member of the population an equal chance of being selected, making inferences from the sample valid for the whole population.

Random Sample (valid)

Every member has equal chance of selectionResults can be generalized to the populationExample: randomly selecting 50 students from a roster

Biased Sample (invalid)

Some members are more likely to be selectedResults may NOT represent the populationExample: only surveying your friends

Random sampling reduces bias and produces trustworthy inferences.

🏫School survey inference
40 students are randomly selected from a school of 800.
30 of the 40 prefer lunch option A.

Proportion = 30/40 = 75%
Estimated number school-wide = 800 × 0.75 = 600 students
p^=3040=0.75⇒800×0.75=600\hat{p} = \frac{30}{40} = 0.75 \Rightarrow 800 \times 0.75 = 600
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Remember This!

Larger random samples produce more reliable inferences. Doubling the sample size roughly halves the margin of error.

✏️ Try It!

In a random sample of 25 fish from a lake, 10 are bass. The lake has about 500 fish. About how many bass are in the lake?

Take Quiz 📝 — 25 Questions