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: \(5\)
CH05-06 lesson
Box Plots Learning Activity
A focused Grade 6 learning session for Box Plots using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 6 mastery of box plots using models, equations, and test-style reasoning.
Student goal: I can solve problems involving box plots.
Helpful first:
Dot Plots and Histograms
Learn the Idea
Box Plots means reading, creating, and explaining displays so data can answer real questions.
- 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.
See the Math
Follow a Worked Example
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: \(7.5\)
Connect It to a Real Situation
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: \(43\)
Avoid Mistakes and Choose a Strategy
- 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.
- 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.
Remember the Key Idea
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.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsA 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 \(20\)
Check answer and explanation
Answer B: \(8\)
IQR \(=\) Q\(_3-\)Q\(_1=22-14=8\).
Use the box plot below to find the median:
- A \(2\)
- B \(3\)
- C \(5\)
- D \(7\)
Check answer and explanation
Answer C: \(5\)
The median is shown by the line inside the box of the box plot.
guided
1 questionWhich value represents Q\(_1\) in the box plot shown?
- A \(1.5\)
- B \(2.5\)
- C \(5.5\)
- D \(9\)
Check answer and explanation
Answer B: \(2.5\)
Q\(_1\) is the left edge of the box in the box plot.
practice
5 questionsA 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 \(12\)
Check answer and explanation
Answer D: \(12\)
The middle 50% is the IQR: Q\(_3-\)Q\(_1=20-8=12\).
Use the box plot below. What is the maximum value?
- A \(1\)
- B \(4\)
- C \(6\)
- D \(8.5\)
Check answer and explanation
Answer D: \(8.5\)
The maximum is shown by the right whisker endpoint of the box plot.
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.
Check answer and explanation
Answer A: Dataset A has a higher center and less spread.
Median measures center; IQR measures spread. Dataset A's median is higher and IQR is smaller (less spread).
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 \(19\)
Check answer and explanation
Answer B: \(8\)
IQR \(=\) Q\(_3-\)Q\(_1=18-10=8\).
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.
Check answer and explanation
Answer A: The lower whisker.
The lower whisker extends from the minimum to Q\(_1\), representing the bottom 25% of the data.
exit
3 questionsUse the box plot below to find the range of the entire dataset:
- A \(1.5\)
- B \(2\)
- C \(4.5\)
- D \(7.5\)
Check answer and explanation
Answer D: \(7.5\)
Range \(=\) max \(-\) min \(= 8 - 0.5 = 7.5\).
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 \(53\)
Check answer and explanation
Answer B: \(16\)
IQR \(=\) Q\(_3-\)Q\(_1=84-68=16\) points.
Which value represents the minimum in this box plot?
- A \(1.5\)
- B \(3\)
- C \(5.5\)
- D \(7\)
Check answer and explanation
Answer A: \(1.5\)
The minimum is the left endpoint of the lower whisker.
