Activity 01
Inquiry Circle: Range vs. IQR
Groups receive two data sets printed on cards: one tightly clustered except for one outlier, one genuinely spread out. They calculate range and IQR for both, then discuss: which set is more consistent? Which measure reflects that better?
Explain what a large range suggests about the consistency of a data set.
Facilitation TipDuring Collaborative Investigation: Range vs. IQR, set a strict three-minute timer for groups to calculate both statistics so the comparison feels urgent and real.
What to look forProvide students with a small data set (e.g., test scores for 5 students). Ask them to calculate the range and IQR. Then, ask: 'What does the range tell you about the spread of these scores? What does the IQR tell you?'
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Activity 02
Think-Pair-Share: Quiz Score Analysis
Present two classes' quiz scores. Both have the same mean, but different IQRs. Pairs discuss which class performed more consistently and what that means for the teacher's interpretation of the results.
Differentiate between range and interquartile range as measures of spread.
Facilitation TipDuring Think-Pair-Share: Quiz Score Analysis, circulate and listen for students who mention ‘middle 50%’ or ‘typical scores’—these phrases signal they are connecting IQR to consistency.
What to look forPresent two data sets with the same range but different IQRs (e.g., Set A: 1, 2, 3, 4, 10; Set B: 4, 5, 6, 7, 10). Ask: 'Which data set is more consistent in its middle values? How do the range and IQR help you answer this?'
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Activity 03
Stations Rotation: Box Plot Building
At each station, students order a data set, find the five-number summary (minimum, Q1, median, Q3, maximum), calculate the IQR, and sketch a basic box plot. Rotating through multiple data sets reinforces the process and builds fluency.
Analyze how outliers affect the range and IQR of a data set.
Facilitation TipDuring Station Rotation: Box Plot Building, place rulers and colored pencils at each station so students can draw precise boxes and whiskers without losing focus.
What to look forGive students a data set with a clear outlier. Ask them to calculate the range. Then, ask them to remove the outlier and recalculate the range. Prompt: 'How did removing the outlier affect the range? Why is the IQR sometimes a better measure of spread for data with outliers?'
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Generate Complete Lesson→A few notes on teaching this unit
Teachers know that students often confuse range and IQR because both sound like ‘spread.’ To fix this, start with messy, small data sets where outliers jump out. Have students calculate range first, then introduce IQR as the fix for those extreme values. Use color coding on box plots to show that the IQR is the width of the box, not the endpoints. Avoid teaching formulas in isolation; anchor them to the visual structure of the box plot.
Successful learning looks like students correctly calculating range and IQR, explaining when each measure is useful, and choosing the right one for different data stories. They should also justify their choices using visuals or written sentences that reference the middle 50% and extreme values.
Watch Out for These Misconceptions
During Collaborative Investigation: Range vs. IQR, watch for students who assume a large range means the entire data set is spread out.
In their groups, have students list the minimum, Q1, median, Q3, and maximum for each data set. Ask them to circle the middle 50% and compare its width to the total length of the range. This forces them to see that the range includes outliers while the IQR does not.
During Station Rotation: Box Plot Building, watch for students who report Q1 and Q3 separately instead of finding their difference.
While students build their box plots, circulate with a dry-erase marker and draw an arrow from Q3 to Q1 on their plot, labeling the arrow ‘IQR = Q3 – Q1.’ This visual reminder turns the calculation into a physical act on the plot.
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