Mathematics · Year 10

Active learning ideas

Comparing Data Sets using Box Plots and Histograms

Active learning works well for comparing data sets because students must physically and visually engage with the spread, center, and shape of data to truly understand differences between groups. Moving beyond calculations to interpret visual displays helps students develop a nuanced understanding of variability and distribution.

• ACARA Content Descriptions
• AC9M10ST02

• 25–50 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 50 min · Small Groups

Inquiry Circle: The Reaction Time Challenge

Students use an online tool to measure their reaction times (e.g., dominant vs. non-dominant hand). In groups, they create back-to-back box plots of the results and write a 'statistical report' comparing the median and spread of the two groups.

Explain how visual displays can be used to argue that two populations are significantly different?

Facilitation Tip

During the Collaborative Investigation, circulate and ask student groups to point to the parts of their human box plot that represent the median and quartiles, ensuring physical movement reinforces abstract concepts.

What to look for

Present students with two box plots comparing the heights of Year 10 students from two different schools. Ask: 'Based on these box plots, which school appears to have taller students overall? Justify your answer using the median and IQR. What are the limitations of comparing only these two statistics?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: Skewness and Stories

The teacher posts four different histograms (e.g., house prices, heights, dice rolls). Groups must match each histogram to a 'story' or data source and explain their reasoning based on the shape (symmetric, left-skewed, right-skewed) to the rest of the class.

Compare the central tendency and spread of two data sets based on their box plots.

Facilitation Tip

For the Gallery Walk, provide sticky notes with sentence stems like 'This skewness suggests...' to scaffold written interpretations of the displays.

What to look for

Provide students with a set of data for two different groups (e.g., test scores). Ask them to construct both a histogram and a box plot for each data set. Then, have them write two sentences comparing the central tendency and spread of the two groups, referencing their graphs.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Think-Pair-Share
• 25 min · Pairs

Think-Pair-Share: The Outlier Debate

Students are given a data set with one extreme outlier. They individually calculate the mean and median, then pair up to discuss which 'average' is a fairer representation of the group. They must agree on a recommendation for a 'news report' based on their findings.

Critique the effectiveness of different graphical displays for comparing data sets.

Facilitation Tip

During the Think-Pair-Share debate, assign one student in each pair to argue for the mean and the other for the median, forcing both perspectives to be considered before consensus.

What to look for

Students work in pairs to compare two real-world data sets (e.g., daily temperatures in two cities). Each student creates a comparative visual display (box plot or histogram). They then swap displays and use a checklist to evaluate their partner's work: 'Is the display clear and correctly labeled? Does it effectively compare the data? Are summary statistics mentioned in the comparison?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach this topic by balancing visual interpretation with hands-on construction of both box plots and histograms. Avoid overemphasizing calculation and instead focus on what each display reveals about the data. Use real-world data sets that naturally lead to questions about center and spread, and encourage students to critique which display better answers their questions. Research shows that students better understand variability when they compare and contrast multiple representations of the same data.

Successful learning is evident when students confidently compare data sets using precise language about median, IQR, spread, and skewness, not just shape or range. They should justify their comparisons with evidence from both box plots and histograms, and recognize when one display reveals information the other does not.

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Watch Out for These Misconceptions

• During the Collaborative Investigation, watch for students assuming that a longer box or whisker contains more data points.

  Use the human box plot to have students count the number of students in each quartile section. Then, measure the distance between quartiles and discuss how spread relates to variability, not quantity of data.

• During the Think-Pair-Share debate, watch for students defaulting to the mean when comparing skewed data sets.

  Provide each pair with a data set like annual incomes and have them calculate both the mean and median. Ask them to explain which measure better represents the 'typical' value and why.

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Methods used in this brief

• Inquiry Circle
• Gallery Walk
• Think-Pair-Share