Statistics (Measures of Center & Variability) • Topic 4 of 4

Random Sampling & Population Inferences

Population: The entire group being studied.

Sample: A subset of the population used to make inferences about the whole.

Random sampling gives every member of the population an equal chance of being selected — this minimizes bias and makes the sample representative.

Sample Type	Biased?	Example
Random from full roster	No (good)	50 students chosen by lottery
First 50 to enter cafeteria	Yes (biased)	Skews towards early arrivers
Friends or acquaintances	Yes (biased)	Similar opinions/backgrounds

Inference: Using sample results to estimate population characteristics. Larger samples give more accurate inferences.

SAMPLING PYRAMID:

  [POPULATION] (all 1000 students)
       |
  [RANDOM SAMPLE] (100 students)
       |
  [MEASURE] (survey, test)
       |
  [INFER ABOUT POPULATION]

GOOD vs BAD SAMPLE:
  Good: Random from complete roster (unbiased)
  Bad:  Only first arrivals, only friends (biased)

Solved Examples

Worked Example

A school has 800 students. You want to know the favorite lunch. Which sample is best? (A) First 50 in cafeteria (B) 50 random from roster (C) 50 friends.

SolutionB is best — randomly selected from the complete roster, so every student has equal chance of being chosen.

Worked Example

A survey of 200 random voters predicts Candidate A will get 55% of votes. Population = 10,000 voters. Estimate votes for A.

Solution55% of 10,000 = 5,500 votes (estimate with some margin of error).

Key Points

Random sample = every population member has equal selection chance
Larger sample size = more accurate inference
Avoid convenience or biased samples
Inferences always have some margin of error

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The entire group being studied is the:

Explanation: Population.

Q2.A part of the population used for study is a:

Explanation: Sample.

Q3.A random sample gives each member:

Explanation: Equal chance.

Q4.Larger samples generally give ___ inferences.

Explanation: More reliable.

Practice more MCQs → 📝 Assignment · 35 marks