Measures of Variability: Range and Interquartile RangeActivities & Teaching Strategies
Active learning helps students grasp measures of variability because sorting, plotting, and manipulating data makes abstract concepts concrete. When students physically rearrange numbers to find quartiles or remove outliers, they see how range and IQR behave differently in real data sets.
Learning Objectives
- 1Calculate the range of a given data set by subtracting the minimum value from the maximum value.
- 2Determine the first quartile (Q1) and third quartile (Q3) for a data set to find the interquartile range (IQR).
- 3Compare the range and IQR of two different data sets to explain which measure better represents the spread of the middle 50% of the data.
- 4Analyze the effect of an outlier on the range and IQR of a data set, explaining why IQR is less affected.
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Pairs Activity: Outlier Hunt
Provide pairs with data sets like student heights; one set includes an outlier. Pairs order data, calculate range and IQR for both, then graph on number lines. Discuss how the outlier changes each measure.
Prepare & details
Explain how the range describes the overall spread of a data set.
Facilitation Tip: During Pairs Activity: Outlier Hunt, circulate to listen for pairs debating whether the range or IQR better describes the data before they calculate.
Setup: Standard classroom seating; students turn to a neighbor
Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs
Small Groups: Survey and Analyze
Groups survey classmates on favorite activities or scores, record 20 data points. Order data to find quartiles, compute range and IQR, and present findings on posters. Compare spreads across groups.
Prepare & details
Differentiate between range and interquartile range in terms of what they measure.
Facilitation Tip: When running Small Groups: Survey and Analyze, ensure each group assigns clear roles so all students engage with ordering data and finding quartiles.
Setup: Standard classroom seating; students turn to a neighbor
Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs
Whole Class: Data Modification Challenge
Display class-generated data on board. As a class, add or remove outliers, recalculate range and IQR each time. Vote on which measure best describes the group.
Prepare & details
Analyze how outliers affect the range compared to the interquartile range.
Facilitation Tip: For Whole Class: Data Modification Challenge, pause after each modification to ask students to predict how the range and IQR will change before recalculating.
Setup: Standard classroom seating; students turn to a neighbor
Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs
Individual: Sports Data Review
Students select Canadian hockey stats, list top 15 points per game. Compute range and IQR, note outlier effects from star players. Write one sentence summary.
Prepare & details
Explain how the range describes the overall spread of a data set.
Setup: Standard classroom seating; students turn to a neighbor
Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs
Teaching This Topic
Teach quartiles first using small, ordered data sets on number lines so students visualize Q1 and Q3 as dividing points. Emphasize that range is a single snapshot of extremes while IQR is a stable 'window' on the middle. Avoid teaching formulas before students understand what the numbers represent; let them derive quartiles from visual grouping.
What to Expect
Successful learning looks like students confidently identifying which measure to use based on data shape, explaining why IQR resists outliers, and applying range and IQR to contextual questions. They should articulate how each measure summarizes spread without relying on vague phrases.
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 Pairs Activity: Outlier Hunt, watch for students claiming the range shows the typical spread because it includes all data points.
What to Teach Instead
Have pairs plot their data on a dot plot and circle the middle cluster to visually demonstrate that range overstates spread and IQR captures the dense center.
Common MisconceptionDuring Pairs Activity: Outlier Hunt, watch for students assuming outliers change the IQR as much as the range.
What to Teach Instead
Ask pairs to remove the outlier and recalculate both measures side-by-side, then compare how range spikes while IQR stays nearly the same.
Common MisconceptionDuring Small Groups: Survey and Analyze, watch for students confusing quartiles with the mean or median.
What to Teach Instead
Ask groups to label each quartile on a number line and write Q1, Q2 (median), and Q3 above the correct points to reinforce their positions.
Assessment Ideas
After Small Groups: Survey and Analyze, present the quick-check data set and ask students to write the range and IQR on mini whiteboards. Collect responses to identify who confuses the two measures.
During Whole Class: Data Modification Challenge, after students modify data sets with and without outliers, facilitate a discussion where they explain which measure they trust more for describing the 'typical' data point and why.
After Individual: Sports Data Review, collect exit tickets to check if students can calculate both measures and articulate one way IQR reveals spread that range misses, using the sports context as evidence.
Extensions & Scaffolding
- Challenge early finishers to create a data set where the range is 40 but the IQR is less than 10, then explain their strategy to a peer.
- Scaffolding for struggling students: Provide pre-sorted data strips and colored markers to highlight Q1, median, and Q3 before they calculate.
- Deeper exploration: Have students research how epidemiologists use IQR to report vaccine efficacy ranges, then present findings to the class.
Key Vocabulary
| Range | The difference between the highest and lowest values in a data set. It shows the total spread of the data. |
| Interquartile Range (IQR) | The difference between the third quartile (Q3) and the first quartile (Q1) of a data set. It represents the spread of the middle 50% of the data. |
| Outlier | A data point that is significantly different from other data points in the set. Outliers can greatly affect the range. |
| Quartile | Values that divide a data set into four equal parts. Q1 is the median of the lower half, and Q3 is the median of the upper half. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
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Unit PlannerMath Unit
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RubricMath Rubric
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