Populations, Samples, Parameters, and Statistics
A free Statistics and Data Analysis lesson from the “Collecting Data” unit, with a worked example and practice problems including step-by-step solutions.
A population is the full group of interest; a sample is the part actually observed. A parameter describes a population, while a statistic describes a sample. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Distinguish population from sample
- Distinguish parameter from statistic
- Use notation and language precisely
Worked example
Problem. A school wants to learn about homework time for all 9th graders and surveys 90 randomly chosen 9th graders. In this study, what is the sample?
- Worked Example: First identify exactly what the question is asking: A school wants to learn about homework time for all 9th graders and surveys 90 randomly chosen 9th graders. In this study, what is the sample?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The sample is the group actually measured.
- Here the measured group is the 90 chosen 9th graders.
Answer: the 90 randomly chosen 9th graders
Practice problems
1. Practice case A: A coach wants to know how all team families feel about practice times and surveys 30 families. What is the population?
Choices: the full group the study wants to learn about · the people surveyed only · the survey question · the sample statistic
Show solution
- Warm-up: First identify exactly what the question is asking: A coach wants to know how all team families feel about practice times and surveys 30 families. What is the population?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The population is the full group of interest.
- The sample is only the group actually surveyed.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: the full group the study wants to learn about
2. Practice case B: A teacher surveys 18 students from one class period. What is the sample?
Choices: everyone the study might care about · the population parameter · the conclusion · the people actually surveyed
Show solution
- Warm-up: First identify exactly what the question is asking: A teacher surveys 18 students from one class period. What is the sample?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The sample is the observed group.
- It is smaller than or equal to the population.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: the people actually surveyed
3. Practice case C: A sample of 75 students has an average screen time of 3.4 hours. The 3.4 hours is a:
Choices: treatment · placebo · sample statistic · population parameter
Show solution
- Warm-up: First identify exactly what the question is asking: A sample of 75 students has an average screen time of 3.4 hours. The 3.4 hours is a:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A statistic is computed from a sample.
- A parameter describes the whole population.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: sample statistic
4. Practice case D: A complete roster shows that 18% of all club members are seniors. The 18% is a:
Choices: survey bias · population parameter · sample statistic · random assignment
Show solution
- Warm-up: First identify exactly what the question is asking: A complete roster shows that 18% of all club members are seniors. The 18% is a:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A parameter describes the whole population.
- The wording says all members of the group were included.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: population parameter
5. Practice case E: In a spreadsheet where each row is one order, what is one case?
Choices: one individual row being studied · the average of a column · the whole population only · the answer choice
Show solution
- Warm-up: First identify exactly what the question is asking: In a spreadsheet where each row is one order, what is one case?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Cases are the individuals or items represented by rows.
- Variables describe something about each case.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: one individual row being studied
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