Introduction
Stem-and-Leaf Plots is an important Grade 6 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 the heights (in cm) of students in a class. What is the minimum height?
| \multicolumn{1}{c|}{Stem} | \multicolumn{1}{c}{Leaf} |
|---|---|
| 14 | 0, 2, 5 |
| 15 | 1, 4, 8, 9 |
| 16 | 3, 6, 7 |
| 17 | 2, 5 |
- A. \(140\) cm
- B. \(142\) cm
- C. \(145\) cm
- D. \(150\) cm
Why it works: The smallest value in the plot is found by taking the smallest stem (14) with its smallest leaf (0), giving \(140\) cm.
Answer: \(140\) cm
Visual Model 2
Question: A stem-and-leaf plot shows daily temperatures (in \(°\)F) recorded during winter: How many temperatures are recorded?
| \multicolumn{1}{c|}{Stem} | \multicolumn{1}{c}{Leaf} |
|---|---|
| 3 | 2, 5, 9 |
| 4 | 1, 4, 6, 8 |
| 5 | 0, 3, 7 |
- A. \(7\)
- B. \(8\)
- C. \(10\)
- D. \(11\)
Why it works: Count all leaves: \(3 + 4 + 3 = 10\) data points.
Answer: \(10\) temperatures
Worked Examples
Example 1
Question: A stem-and-leaf plot of student test scores is given: What is the mode of the test scores?
| \multicolumn{1}{c|}{Stem} | \multicolumn{1}{c}{Leaf} |
|---|---|
| 6 | 5, 8 |
| 7 | 1, 3, 4, 6, 9 |
| 8 | 0, 2, 5, 7 |
| 9 | 1, 4, 8 |
- A. \(70\)
- B. \(74\)
- C. \(80\)
- D. No single mode
- Each stem has multiple leaves but no single score repeats more than once, so there is no single mode.
Answer: No single mode
Example 2
Question: A fitness coach records the number of push-ups done by \(11\) athletes: Which interval contains the most data points?
| \multicolumn{1}{c|}{Stem} | \multicolumn{1}{c}{Leaf} |
|---|---|
| 2 | 3, 5, 8, 9 |
| 3 | 1, 4, 6, 7 |
| 4 | 2, 5, 8 |
- A. 20--29
- B. 30--39
- C. Both have equal counts
- D. 40--49
- Count the leaves on each stem: stem \(2\) (the 20s) has \(4\) leaves, stem \(3\) (the 30s) has \(4\) leaves, and stem \(4\) (the 40s) has \(3\) leaves.
- Stems \(2\) and \(3\) are tied for the most data points, so the correct response is that both intervals have equal counts.
Answer: Both have equal counts
Example 3
Question: A researcher gathers data on the number of hours 10 students study per week: What is the mean (average) number of hours studied?
| \multicolumn{1}{c|}{Stem} | \multicolumn{1}{c}{Leaf} |
|---|---|
| 1 | 2, 5, 8 |
| 2 | 1, 3, 4, 6, 9 |
| 3 | 0, 2 |
- A. \(22\) hours
- B. \(25\) hours
- C. \(24\) hours
- D. \(23\) hours
- Sum: \(12 + 15 + 18 + 21 + 23 + 24 + 26 + 29 + 30 + 32 = 230\).
- Mean: \(230 \div 10 = 23\) hours.
Answer: \(23\) hours
Real-World Word Problems
Problem 1
Question: Raw data for number of books read by 8 students: \(12, 18, 15, 12, 20, 15, 14, 19\). If you were to create a stem-and-leaf plot, how many leaves would be in stem \(1\)?
- A. \(5\)
- B. \(6\)
- C. \(7\)
- D. \(8\)
Why it works: Numbers in the 10s: \(12, 18, 15, 12, 20, 15, 14, 19\). Those with stem \(1\): \(12, 18, 15, 12, 15, 14\) (6 values).
Answer: \(6\) leaves
Problem 2
Question: A store records daily sales (in hundreds of dollars): How many days had sales of at least \($900\) (stem \(\geq 9\))?
| \multicolumn{1}{c|}{Stem} | \multicolumn{1}{c}{Leaf} |
|---|---|
| 8 | 2, 5, 7 |
| 9 | 1, 3, 4, 6, 8 |
| 10 | 2, 5, 7 |
- A. \(3\)
- B. \(5\)
- C. \(11\)
- D. \(8\)
Why it works: Stem \(9\) has 5 leaves and stem \(10\) has 3 leaves, totaling \(5 + 3 = 8\) days.
Answer: \(8\) days
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 of test scores has stem \(7\) with leaves \(2, 5, 8\). Which values are represented?
- A. \(27, 57, 87\)
- B. \(72, 75, 78\)
- C. \(70, 71, 72\)
- D. \(7.2, 7.5, 7.8\)
Question 2
Using the same stem-and-leaf plot from Question 2, what is the maximum height?
- A. \(165\) cm
- B. \(167\) cm
- C. \(175\) cm
- D. \(177\) cm
Question 3
Using the same stem-and-leaf plot from Question 2, what is the range of heights?
- A. \(35\) cm
- B. \(30\) cm
- C. \(25\) cm
- D. \(40\) cm
Question 4
Using the temperature data from Question 5, what is the median temperature?
- A. 45°F
- B. 50°F
- C. 48°F
- D. 46°F
Question 5
Using the temperature data from Question 5, which temperature appears most frequently (the mode)?
- A. No mode
- B. 41°F
- C. 44°F
- D. 48°F
Question 6
In the stem-and-leaf plot above (Question 8), how many scores are in the 70s?
- A. \(3\)
- B. \(4\)
- C. \(5\)
- D. \(6\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(72, 75, 78\)
In a stem-and-leaf plot, each leaf combines with the stem to form a value. Stem \(7\) with leaves \(2, 5, 8\) represents \(72, 75, 78\).
Question 2
Answer: \(175\) cm
The largest stem is 17, and the largest leaf for that stem is 5, so the maximum is \(175\) cm.
Question 3
Answer: \(35\) cm
Range = Max \(-\) Min = \(175 - 140 = 35\) cm.
Question 4
Answer: 45°F
Order the data: \(32, 35, 39, 41, 44, 46, 48, 50, 53, 57\). With \(10\) values (an even count), the median is the average of the \(5\)th and \(6\)th values: \((44 + 46) \div 2 = 45°\)F.
Question 5
Answer: No mode
Each temperature appears exactly once in the data, so there is no mode (or all are modes).
Question 6
Answer: \(5\) scores
Stem \(7\) has leaves \(1, 3, 4, 6, 9\), which is \(5\) leaves total.
Connection to Standards
This lesson supports Grade 6 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.
