How can a table summarize choices?
You will be able to: Build a frequency table and interpret a sample proportion in context.
How can a table summarize choices?
Of 20 club members, 10 walk, 6 take a bus and 4 bike. A table makes both the count and share of each choice visible.
A useful starting point: Who is measured, and what kind of variable is it? →
Words and symbols before equations
- Frequency
- Number of observations in a category.
- Relative frequency
- Category count divided by total count.
- Proportion p̂
- A sample share between 0 and 1.
- Percentage
- A proportion multiplied by 100.
What this picture assumes
One mutually exclusive travel choice per student: walk 10, bike 4, bus adjustable. Bar baseline is zero. Percentages use the current total.
Read the picture in three steps
- Read the axes and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- Total 20. Walk 50%, bus 30%, bike 20%. Each count is one student.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the mathematics
Use categories that cover all observations without double counting. If the question allows multiple selections, a simple one-choice total is no longer the correct model.
Divide each count by the same total: 10/20=0.50, 6/20=0.30 and 4/20=0.20. Proportions add to 1, apart from rounding.
A sample proportion describes the sample. To infer a population preference, inspect how the sample was selected and which people may be absent.
A worked example, step by step
A survey gives 12 paperback, 6 ebook and 2 audio preferences among 20 respondents. What proportion chose ebook?
- Check that each respondent supplied one preference.
- Total count is 12+6+2=20.
- The ebook proportion is 6/20=0.30, or 30%.
- Say 30% of these respondents chose ebook; do not claim 30% of everyone without a justified sampling plan.
The denominator is the relevant total, not the count of the largest category.
If 8 of 40 students choose art, what is p̂?
Compare with an explanation
8/40=0.20, or 20% of the sampled students.
Predict. Change one thing. Explain.
Increase the bus count while keeping walk and bike counts fixed. Explain why their counts stay fixed but their proportions fall.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Total 20. Walk 50%, bus 30%, bike 20%. Each count is one student.
| Choice | Count | Proportion | Pie angle |
|---|---|---|---|
| Walk | 10 | 0.5 | 180° |
| Bus | 6 | 0.3 | 108° |
| Bike | 4 | 0.2 | 72° |
One mutually exclusive travel choice per student: walk 10, bike 4, bus adjustable. Bar baseline is zero. Percentages use the current total.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using the data values, graph scales, summary statistics or study-design conditions. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionAmong 25 respondents, 10 choose A, 8 choose B and 7 choose C. Construct relative frequencies and explain one limitation.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Use total 25.
- 1 point: A: 0.40; B: 0.32; C: 0.28.
- 1 point: The shares sum to 1, or 100%.
- 1 point: They describe respondents; generalization depends on collection and nonresponse.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1How do you calculate relative frequency?
Divide category count by the total.
RECALL 2Can a sample proportion exceed 1?
No, when it is a share of the stated total.
RECALL 3What should a one-choice table total?
The sample size in counts and 1 in proportions.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How can a table summarize choices?
- Relative frequency = count / total.
- Percentage = 100 × relative frequency.
- For exclusive, exhaustive categories, proportions sum to 1.
Remember: The denominator is the relevant total, not the count of the largest category.
Conditions: One mutually exclusive travel choice per student: walk 10, bike 4, bus adjustable. Bar baseline is zero. Percentages use the current total.
Refresh Kid · AP Statistics Unit 1 · Objectives 1.3.A, 1.3.B · Review edition
Framework, scope and review status
Mapped to College Board, AP Statistics CED, Topic 1.3, objectives 1.3.A, 1.3.B. Framework effective Fall 2026, checked September 17, 2026. Unit 1 includes one-variable data and data collection; it is part of the revised five-unit course.
Examples and datasets are synthetic, independently authored teaching material. Quartile calculations state a median-of-halves convention. Outlier screens identify values to investigate, not data to discard. Random selection and random assignment have different inferential roles. These lessons introduce design and descriptive reasoning; formal inference comes in later units.
The Organic Chemistry Tutor companion title and destination were checked; the full video was not reviewed. Khan Academy’s destination was checked, but its lesson content was not fully readable by the research tool. OpenStax provides optional reference reading. No provider scripts, questions or graphics were copied. Refresh Kid is not affiliated with these providers.
GitHub’s 3D website collection informed optional spatial inspection. Our original sampling model uses self-hosted Three.js with its MIT license. It shows labeled units in four groups; camera rotation does not change the sampling procedure. Quantitative graphs remain 2D to avoid perspective distortion. Complete labeled diagrams, selected IDs and explanations remain available without 3D.
Independent teacher review and observation of students remain pending. Technical checks do not certify statistical accuracy, accessibility or learning effectiveness. This is a review edition.
Released AP Statistics questions and scoring guides are optional. Older exams use the earlier framework, so check alignment before selecting parts. All practice on this page is original, not official AP material.
Learn → Explore → Practice → Review is informed by the IES learning guide. This implementation has not yet been evaluated with learners.
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