Introduction
Box 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 box plots.
What Is Box Plots?
Box 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 Box 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: Use the box plot below to find the median:
- A. \(2\)
- B. \(3\)
- C. \(5\)
- D. \(7\)
Why it works: The median is shown by the line inside the box of the box plot.
Answer: \(5\)
Visual Model 2
Question: Which value represents Q\(_1\) in the box plot shown?
- A. \(1.5\)
- B. \(2.5\)
- C. \(5.5\)
- D. \(9\)
Why it works: Q\(_1\) is the left edge of the box in the box plot.
Answer: \(2.5\)
Worked Examples
Example 1
Question: Use the box plot below. What is the maximum value?
- A. \(1\)
- B. \(4\)
- C. \(6\)
- D. \(8.5\)
- The maximum is shown by the right whisker endpoint of the box plot.
Answer: \(8.5\)
Example 2
Question: Use the box plot below to find the range of the entire dataset:
- A. \(1.5\)
- B. \(2\)
- C. \(4.5\)
- D. \(7.5\)
- Range \(=\) max \(-\) min \(= 8 - 0.5 = 7.5\).
Answer: \(7.5\)
Example 3
Question: Which value represents the minimum in this box plot?
- A. \(1.5\)
- B. \(3\)
- C. \(5.5\)
- D. \(7\)
- The minimum is the left endpoint of the lower whisker.
Answer: \(1.5\)
Real-World Word Problems
Problem 1
Question: The five-number summary of student test scores is: min \(= 55\), Q\(_1=70\), median \(= 78\), Q\(_3=85\), max \(= 98\). How many points is the range?
- A. \(15\)
- B. \(23\)
- C. \(43\)
- D. \(78\)
Why it works: Range \(=\) max \(-\) min \(= 98 - 55 = 43\) points.
Answer: \(43\)
Problem 2
Question: A student reads a box plot and says: "The median is 22, so 22 is in the middle of the data." Which best describes the error?
- A. The median is not in the middle of the data.
- B. The median is a data value that separates the lower half from the upper half, not necessarily the center of the spread.
- C. The median is always the average of two numbers.
- D. The median cannot be determined from a box plot.
Why it works: The median divides data into two equal groups by count (50% below, 50% above), but may not be the center of the spread on the number line. For asymmetric distributions, the median can be off-center.
Answer: The median is a data value that separates the lower half from the upper half, not necessarily the center of the spread
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 box plot shows the following five-number summary: minimum \(= 10\), Q\(_1=14\), median \(= 18\), Q\(_3=22\), maximum \(= 30\). What is the interquartile range (IQR)?
- A. \(4\)
- B. \(8\)
- C. \(12\)
- D. \(20\)
Question 2
A dataset has Q\(_1=8\) and Q\(_3=20\). What is the range of the middle 50% of the data?
- A. \(8\)
- B. \(28\)
- C. \(20\)
- D. \(12\)
Question 3
Compare two box plots: Dataset A has median 50 and IQR 15; Dataset B has median 45 and IQR 20. Which statement is true?
- A. Dataset A has a higher center and less spread.
- B. Dataset A has a lower center and more spread.
- C. Both datasets have the same center.
- D. Dataset B is more skewed.
Question 4
A dataset has the five-number summary: min \(= 6\), Q\(_1=10\), median \(= 13\), Q\(_3=18\), max \(= 25\). Which represents the IQR?
- A. \(4\)
- B. \(8\)
- C. \(13\)
- D. \(19\)
Question 5
Which part of a box plot represents the bottom 25% of the data?
- A. The lower whisker.
- B. The left side of the box.
- C. The median line.
- D. The upper whisker.
Question 6
The five-number summary for test scores is: min \(= 42\), Q\(_1=68\), median \(= 76\), Q\(_3=84\), max \(= 95\). How many points separate Q\(_1\) from Q\(_3\)?
- A. \(8\)
- B. \(16\)
- C. \(26\)
- D. \(53\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(8\)
IQR \(=\) Q\(_3-\)Q\(_1=22-14=8\).
Question 2
Answer: \(12\)
The middle 50% is the IQR: Q\(_3-\)Q\(_1=20-8=12\).
Question 3
Answer: Dataset A has a higher median (50 vs 45) and smaller IQR (15 vs 20)
Median measures center; IQR measures spread. Dataset A's median is higher and IQR is smaller (less spread).
Question 4
Answer: \(8\)
IQR \(=\) Q\(_3-\)Q\(_1=18-10=8\).
Question 5
Answer: The lower whisker
The lower whisker extends from the minimum to Q\(_1\), representing the bottom 25% of the data.
Question 6
Answer: \(16\)
IQR \(=\) Q\(_3-\)Q\(_1=84-68=16\) points.
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
Box 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.
