Statistics Final Exam
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
The final exam is a cumulative Statistics and Data Analysis readiness test with AP and college-style interpretation mixed into computation.
What you'll learn
- Review the major skills from this part of the course
- Choose an appropriate statistical method
- Explain results in context
Worked example
Problem. Which variable is categorical?
- Worked Example: First identify exactly what the question is asking: Which variable is categorical?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Categorical variables name groups or labels.
- Favorite app is a label rather than a measurement.
Answer: Favorite app
Practice problems
1. Review case A: Which variable is categorical?
Choices: Minutes studied · Number of siblings · Favorite app · Height in inches
Show solution
- Final Review: First identify exactly what the question is asking: Which variable is categorical?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Categorical variables name groups or labels.
- Favorite app is a label rather than a measurement.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Favorite app
2. Review case B: Which variable is quantitative?
Choices: Device brand · Time in minutes · Eye color · Lunch choice
Show solution
- Final Review: First identify exactly what the question is asking: Which variable is quantitative?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Quantitative variables measure amounts.
- Time in minutes is numerical and can be averaged.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Time in minutes
3. Review case C: A frequency table shows 8 first-choice votes, 12 second-choice votes, and 6 third-choice votes. How many responses are in the table?
Show solution
- Final Review: First identify exactly what the question is asking: A frequency table shows 8 first-choice votes, 12 second-choice votes, and 6 third-choice votes. How many responses are in the table?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Add all category counts: 8 + 12 + 6.
- The total is 26.
- Check the result by substituting or estimating: the response should match 26 and make sense in the original problem.
Answer: 26
4. Review case D: A box plot has Q1 = 9, median = 11, and Q3 = 13. Find the IQR.
Show solution
- Final Review: First identify exactly what the question is asking: A box plot has Q1 = 9, median = 11, and Q3 = 13. Find the IQR.
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- IQR measures the spread of the middle half.
- 13 - 9 = 4.
- Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.
Answer: 4
5. Review case E: Find the median of 17, 8, 20, 11, 14.
Show solution
- Final Review: First identify exactly what the question is asking: Find the median of 17, 8, 20, 11, 14.
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Order the data from least to greatest.
- The middle value is 14.
- Check the result by substituting or estimating: the response should match 14 and make sense in the original problem.
Answer: 14
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