How can a graph keep individual values visible?
You will be able to: Construct a dotplot and stem-and-leaf plot with a meaningful key.
How can a graph keep individual values visible?
Five classmates take 12, 12, 14, 17 and 21 minutes to reach school. Two have the same time, but both students must remain in the graph.
A useful starting point: What makes a categorical graph honest? →
Words and symbols before equations
- Dotplot
- One dot per observation above its measured value.
- Stem
- The leading digit or digits in a stem-and-leaf display.
- Leaf
- The final recorded digit of an observation.
- Key
- A statement explaining how a stem and leaf reconstruct a value.
What this picture assumes
Synthetic travel times in minutes. One dot per observation; all graphs use the same 0–16 minute axis. Stem key: 1 : 2 means 12 minutes.
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.
- n=12; mean 5.833, median 4.5, sample s 3.996, IQR 5, range 12 minutes.
- 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 a number line with equal distances for equal differences in time. Stack repeated values rather than hiding a dot.
With tens as stems, write stem 1 with leaves 2,2,4,7 and stem 2 with leaf 1. The key “1 : 2 means 12 minutes” fixes both place value and units.
Both displays retain individual observations. Order leaves and include repeated leaves. Gaps on the numerical axis should remain visible rather than compressing missing values.
A worked example, step by step
Make a stemplot for 23, 25, 25, 31 and 34 minutes.
- Order the values: 23,25,25,31,34.
- Use stem 2 with leaves 3,5,5; stem 3 with leaves 1,4.
- State the key: 2 : 3 means 23 minutes.
- There are five leaves, matching five observations; 25 appears twice.
A leaf is an observation, not just a distinct value. Repetitions count.
Why must two 12-minute waits produce two dots?
Compare with an explanation
They represent two observations, even though the measured values match.
Predict. Change one thing. Explain.
Switch between the small datasets and read every value from the dotplot. Compare with the listed stem-and-leaf display and check the total number of observations.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
n=12; mean 5.833, median 4.5, sample s 3.996, IQR 5, range 12 minutes.
| Summary | Value |
|---|---|
| Data | 2, 2, 3, 3, 4, 4, 5, 5, 6, 10, 12, 14 |
| Mean | 5.833 |
| Median | 4.5 |
| Sample variance | 15.97 squared units |
| Sample s | 3.996 |
| Q₁ / Q₃ | 3 / 8 |
| Stem | Ordered leaves · key 1 : 2 = 12 minutes |
|---|---|
| 0 | 2 2 3 3 4 4 5 5 6 |
| 1 | 0 2 4 |
Synthetic travel times in minutes. One dot per observation; all graphs use the same 0–16 minute axis. Stem key: 1 : 2 means 12 minutes.
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 questionFor 11, 13, 13, 19 and 20 seconds, describe the dotplot, write the stemplot and its key.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Plot one dot at 11, two at 13, one at 19 and one at 20.
- 1 point: Use stem 1 with leaves 1,3,3,9 and stem 2 with leaf 0.
- 1 point: Key: 1 : 1 means 11 seconds.
- 1 point: Five dots and five leaves retain all five observations.
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 1What does one dot represent?
One observation.
RECALL 2Why include a key?
To identify place value and measurement units.
RECALL 3Which display preserves exact recorded values?
A dotplot or a correctly keyed stemplot.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How can a graph keep individual values visible?
- One dot or leaf per observation.
- Use equal numerical spacing.
- Always include units and a stem key.
Remember: A leaf is an observation, not just a distinct value. Repetitions count.
Conditions: Synthetic travel times in minutes. One dot per observation; all graphs use the same 0–16 minute axis. Stem key: 1 : 2 means 12 minutes.
Refresh Kid · AP Statistics Unit 1 · Objectives 1.5.A · Review edition
Framework, scope and review status
Mapped to College Board, AP Statistics CED, Topic 1.5, objectives 1.5.A. 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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