Introduction
Stem-and-Leaf Plots is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with stem-and-leaf plots.
What Is Stem-and-Leaf Plots?
Stem-and-Leaf Plots means reading, creating, and explaining displays so data can answer real questions.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Stem-and-Leaf Plots
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the title, labels, and scale before answering.
- Use the scale value instead of counting marks as ones when the graph is scaled.
- Compare categories by subtracting or adding values from the display.
- Explain what the data shows in a complete sentence.
Visual Models
Visual Model 1
Question: The stem-and-leaf plot below shows test scores. What is the minimum score?
| Stem | Leaves |
|---|---|
| 4 | 2, 6, 8 |
| 5 | 1, 3, 7, 9 |
| 6 | 0, 5, 5, 8 |
| 7 | 2, 4, 6 |
- A. \(42\)
- B. \(41\)
- C. \(40\)
- D. \(48\)
Why it works: The smallest stem is \(4\) with the smallest leaf \(2\), giving \(42\).
Answer: \(42\)
Visual Model 2
Question: The stem-and-leaf plot below shows test scores. What is the maximum score?
| Stem | Leaves |
|---|---|
| 4 | 2, 6, 8 |
| 5 | 1, 3, 7, 9 |
| 6 | 0, 5, 5, 8 |
| 7 | 2, 4, 6 |
- A. \(76\)
- B. \(77\)
- C. \(79\)
- D. \(86\)
Why it works: The largest stem is \(7\) with the largest leaf \(6\), giving \(76\).
Answer: \(76\)
Worked Examples
Example 1
Question: The stem-and-leaf plot shows heights (in cm) of students: How many students are represented?
| Stem | Leaves |
|---|---|
| 15 | 2, 5, 8 |
| 16 | 1, 3, 6, 9 |
| 17 | 0, 4, 7 |
| 18 | 2, 5 |
- A. \(8\)
- B. \(11\)
- C. \(12\)
- D. \(14\)
- Count all leaves: \(3 + 4 + 3 + 2 = 12\) data points.
Answer: \(12\)
Example 2
Question: The stem-and-leaf plot shows: How many data values fall between \(30\) and \(40\) (inclusive)?
| Stem | Leaves |
|---|---|
| 2 | 3, 5, 9 |
| 3 | 1, 4, 4, 7 |
| 4 | 2, 6 |
- A. \(2\)
- B. \(3\)
- C. \(4\)
- D. \(5\)
- Values in the range: \(31, 34, 34, 37\) (all from stem \(3\)) \(= 4\) values.
Answer: \(4\)
Example 3
Question: The stem-and-leaf plot displays class test scores: What is the median score?
| Stem | Leaves |
|---|---|
| 7 | 2, 5, 8, 8 |
| 8 | 1, 3, 5, 6, 9 |
| 9 | 0, 2, 4, 7 |
- A. \(85\)
- B. \(84\)
- C. \(83\)
- D. \(82\)
- There are \(13\) values (odd).
- Ordered: \(72, 75, 78, 78, 81, 83, 85, 86, 89, 90, 92, 94, 97\).
- The 7th value is \(85\).
Answer: \(85\)
Real-World Word Problems
Problem 1
Question: A student creates a stem-and-leaf plot with stems \(6, 7, 8\) and counts \(3\) leaves under each stem. What is the total number of data points?
- A. \(3\)
- B. \(6\)
- C. \(9\)
- D. \(10\)
Why it works: Total data points \(= 3 + 3 + 3 = 9\).
Answer: \(9\)
Problem 2
Question: A stem-and-leaf plot of student heights (in cm) shows: What is the mean of the data? (Rounded to nearest whole number)
| Stem | Leaves |
|---|---|
| 14 | 8, 9 |
| 15 | 0, 2, 4, 6, 8 |
| 16 | 1, 3, 5, 7, 9 |
| 17 | 0, 2, 4 |
- A. \(158\)
- B. \(159\)
- C. \(160\)
- D. \(161\)
Why it works: Sum: \(148 + 149 + 150 + 152 + 154 + 156 + 158 + 161 + 163 + 165 + 167 + 169 + 170 + 172 + 174 = 2388\). Mean \(= 2388 / 15 = 159.2 \approx 159\).
Answer: \(159\)
Common Mistakes
- Ignoring the graph scale.
- Reading the wrong category or axis label.
- Answering a comparison question without subtracting.
- Writing a number without explaining what it represents.
Strategy Tips
- Circle the scale before using the graph.
- Write down the value for each category you compare.
- Use addition for totals and subtraction for differences.
- Answer in words so the data result has meaning.
Practice Questions
Question 1
A stem-and-leaf plot has stem \(3\) with leaves \(2, 5, 7, 8\). Which values does this represent?
- A. \(23, 35, 37, 38\)
- B. \(32, 35, 37, 38\)
- C. \(2, 5, 7, 8\)
- D. \(3.2, 3.5, 3.7, 3.8\)
Question 2
A stem-and-leaf plot has stems \(5, 6, 7\) with leaves: What is the range of the data?
- A. Stem \(5\): \(1, 4, 7\)
- B. Stem \(6\): \(0, 3, 8\)
- C. Stem \(7\): \(2, 6, 9\)
Question 3
In a stem-and-leaf plot, the stem represents the tens digit and leaves represent the ones digit. If a value is \(67\), what stem and leaf should be written?
- A. Stem \(6\), Leaf \(7\)
- B. Stem \(7\), Leaf \(6\)
- C. Stem \(60\), Leaf \(7\)
- D. Stem \(67\), Leaf \(1\)
Question 4
A data set has values: \(12, 15, 15, 18, 21, 23, 24, 28\). Which is the correct stem-and-leaf plot?
- A. Stem \(1\): \(2, 5, 5, 8\); Stem \(2\): \(1, 3, 4, 8\)
- B. Stem \(1\): \(1, 2, 5, 5\); Stem \(2\): \(1, 3, 4, 8\)
- C. Stem \(1\): \(2, 5, 5, 8\); Stem \(2\): \(3, 4, 8, 1\)
- D. Stem \(1\): \(1, 2, 3, 4\); Stem \(2\): \(1, 5, 5, 8\)
Question 5
The stem-and-leaf plot shows: What is the mode?
| Stem | Leaves |
|---|---|
| 10 | 1, 5, 7 |
| 11 | 2, 3, 8, 9 |
| 12 | 0, 4, 6 |
- A. \(112\)
- B. \(118\)
- C. \(119\)
- D. No mode
Question 6
Three-digit data in a stem-and-leaf plot with stem \(14\) and leaves \(2, 5, 8\) represents which values?
- A. \(142, 145, 148\)
- B. \(1402, 1405, 1408\)
- C. \(14.2, 14.5, 14.8\)
- D. \(214, 514, 814\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(32, 35, 37, 38\)
Each leaf combines with its stem: stem \(3\) + leaf \(2\) = \(32\), stem \(3\) + leaf \(5\) = \(35\), etc.
Question 2
Answer: \(25\)
Minimum is \(51\), maximum is \(76\). Range \(= 76 - 51 = 25\).
Question 3
Answer: Stem \(6\), Leaf \(7\)
The tens digit (\(6\)) is the stem; the ones digit (\(7\)) is the leaf.
Question 4
Answer: Stem \(1\): \(2, 5, 5, 8\); Stem \(2\): \(1, 3, 4, 8\)
Leaves must be listed in order and correspond to the tens digit (stem).
Question 5
Answer: No mode
Each value appears exactly once, so there is no repeating value. There is no mode.
Question 6
Answer: \(142, 145, 148\)
With a two-digit stem (\(14\)), leaves are the ones place: \(142, 145, 148\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Stem-and-Leaf Plots becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Read the scale before reading the answer.
