Box Plots and Interquartile RangeActivities & Teaching Strategies
Active construction of box plots helps Year 11 students move beyond abstract definitions to see how quartiles partition data. When learners order raw scores and mark Q1, median, and Q3 themselves, the five-number summary becomes a tool they trust, not just a formula they memorize.
Learning Objectives
- 1Calculate the interquartile range (IQR) for a given dataset.
- 2Construct a box plot accurately from a five-number summary.
- 3Compare and contrast the central tendency and spread of two datasets using their box plots.
- 4Identify potential outliers in a dataset using the 1.5 * IQR rule.
- 5Explain why the median is a more appropriate measure of central tendency than the mean for skewed data.
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Pair Plotting: Class Test Scores
Provide pairs with two lists of 20 test scores each. They order data, find quartiles and median, then sketch box plots side-by-side. Pairs note differences in spread and outliers before sharing with the class.
Prepare & details
Justify why the median is often a better measure of central tendency than the mean for skewed data.
Facilitation Tip: During Pair Plotting, have students swap datasets before plotting so they must read each other’s ordered lists aloud, reinforcing precision.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Small Group Comparison: Athlete Performances
Give small groups datasets on 100m sprint times for two teams. Groups construct box plots, calculate IQRs, and discuss which team has greater consistency. They present findings using key questions on a whiteboard.
Prepare & details
Differentiate between the range and the interquartile range as measures of spread.
Facilitation Tip: In Small Group Comparison, assign each group one class’s scores and one athlete’s performance measures so debates focus on concrete numbers rather than assumptions.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Whole Class Outlier Hunt: Real Data Challenge
Display a large dataset on the board, such as household incomes. Class votes on potential outliers, then constructs a box plot together to verify using IQR rule. Discuss impacts on mean versus median.
Prepare & details
Compare two datasets using box plots, drawing conclusions about their distributions.
Facilitation Tip: For Whole Class Outlier Hunt, give three different IQR multipliers (1.0, 1.5, 2.0) on the same dataset so students see how threshold choices change the outlier list.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Individual Interpretation: Skewed Distributions
Students receive printed box plots of skewed data like incomes or ages. Individually, they justify median use over mean and compare spreads. Follow with pair shares to refine explanations.
Prepare & details
Justify why the median is often a better measure of central tendency than the mean for skewed data.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Teaching This Topic
Start with a human box plot on the floor using students’ heights or shoe sizes; this kinesthetic hook makes quartiles tangible. Avoid rushing to the formula—instead, let learners derive Q1 and Q3 from medians of halves, which reduces later confusion about quartile placement. Research shows that students who physically arrange data before plotting score higher on interpretation tasks.
What to Expect
Students will confidently order data, compute quartiles and IQR, and draw accurate box plots by the end of the sequence. They will also interpret spread and skewness and justify decisions about outliers using clear reasoning.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Pair Plotting: Class Test Scores, watch for students who assume the box plot’s box height equals the number of students in that quartile.
What to Teach Instead
Have students label the quartile boundaries with the actual minimum, Q1, median, Q3, and maximum values, then count how many data points fall in each section to prove the box height does not reflect frequency.
Common MisconceptionDuring Small Group Comparison: Athlete Performances, watch for students who interpret a wider box as higher overall performance rather than greater spread.
What to Teach Instead
Ask groups to calculate the median heights of both distributions and compare them before discussing box width, reinforcing that spread and center are separate features.
Common MisconceptionDuring Whole Class Outlier Hunt: Real Data Challenge, watch for students who treat any value beyond 1.5×IQR as an automatic error to remove.
What to Teach Instead
Direct students to write a one-sentence context-based justification for each outlier, such as ‘A 10-second 100m time could be valid for an elite sprinter,’ before deciding whether to investigate further.
Assessment Ideas
After Pair Plotting: Class Test Scores, collect students’ five-number summaries and box plots. Check that quartiles are correctly calculated from the ordered data and that the plot is drawn to scale with median and quartiles clearly marked.
During Small Group Comparison: Athlete Performances, circulate and listen for groups that compare medians and IQR ranges while avoiding statements like ‘the higher box means better scores.’ Ask guiding questions to refocus their language on spread rather than rank.
After Whole Class Outlier Hunt: Real Data Challenge, give each student a 10-value dataset. Ask them to calculate the IQR, identify outliers using 1.5×IQR, and write one sentence explaining why the median is a more representative center for skewed data.
Extensions & Scaffolding
- Challenge: Ask students to generate a dataset with a specified IQR but different skewness, then justify why the IQR alone cannot reveal shape.
- Scaffolding: Provide partially ordered lists and pre-marked medians so students focus on identifying Q1 and Q3 without the sorting burden.
- Deeper exploration: Have students collect their own data (e.g., reaction times), calculate IQR for multiple samples, and create a class dot plot overlaying all box plots to discuss sampling variability.
Key Vocabulary
| Interquartile Range (IQR) | The difference between the upper quartile (Q3) and the lower quartile (Q1) of a dataset, representing the spread of the middle 50% of the data. |
| Box Plot | A graphical representation of data that displays the five-number summary: minimum, Q1, median, Q3, and maximum. |
| Median | The middle value in a dataset when the data is ordered from least to greatest. It divides the data into two equal halves. |
| Quartiles | Values that divide a dataset into four equal parts. Q1 is the median of the lower half, and Q3 is the median of the upper half. |
| Outlier | A data point that is significantly different from other observations in the dataset, often identified using the IQR rule. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
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RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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