Variables, Cases, and Data Types
A free Statistics and Data Analysis lesson from the “Data Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Statistics starts by naming what the rows, columns, and measurements mean. Cases are the individuals or items being studied. Variables describe something about each case, and the variable type determines which displays and summaries make sense. 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
- Identify cases and variables
- Classify categorical and quantitative variables
- Connect a data table to the question being asked
Worked example
Problem. Which variable is quantitative?
- Quantitative variables measure amounts.
- Time in minutes is numerical and can be averaged.
Answer: Time in minutes
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: Which variable is quantitative?
Choices: Lunch choice · Device brand · Time in minutes · Eye color
Show solution
- Quantitative variables measure amounts.
- Time in minutes is numerical and can be averaged.
Answer: Time in minutes
2. Practice case B: A frequency table shows 7 first-choice votes, 12 second-choice votes, and 5 third-choice votes. How many responses are in the table?
Show solution
- Add all category counts: 7 + 12 + 5.
- The total is 24.
Answer: 24
3. Practice case C: A bar chart has 8 votes for A out of 27 total votes. About what percent chose A? Enter the nearest whole percent.
Show solution
- Relative frequency is count divided by total.
- 8 / 27 is about 30%.
Answer: 30
4. Practice case D: Which display is best for comparing counts across categories?
Choices: Histogram · Box plot · Residual plot · Bar chart
Show solution
- A bar chart compares category counts.
- Histograms and box plots are for quantitative distributions.
Answer: Bar chart
5. Practice case E: A histogram is used mainly to show:
Choices: the cause of an association · the treatment in an experiment · the shape of quantitative data · the exact value of a population parameter
Show solution
- Histograms group quantitative values into intervals.
- That reveals distribution shape.
Answer: the shape of quantitative data
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