Dot Plots, Histograms, and Distribution Shape
A free Statistics and Data Analysis lesson from the “Data Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Quantitative data has shape. Dot plots show individual values, while histograms group values into intervals. Both help reveal whether a distribution is symmetric, skewed, clustered, or unusual. 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
- Choose a display for quantitative data
- Describe shape, cluster, gap, and outlier patterns
- Read intervals from a histogram
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: Time in minutes · Eye color · Lunch choice · Device brand
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: Residual plot · Bar chart · Histogram · Box plot
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 shape of quantitative data · the exact value of a population parameter · the cause of an association · the treatment in an experiment
Show solution
- Histograms group quantitative values into intervals.
- That reveals distribution shape.
Answer: the shape of quantitative data
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