Mathematics · Year 9

Active learning ideas

Interpreting Data Displays and Outliers

Active learning works for this topic because students need to physically manipulate data displays to truly grasp their meaning. When students sort, sketch, and debate displays like histograms and box plots with their hands and voices, abstract concepts like skewness and outliers become concrete and memorable. This hands-on approach builds the spatial reasoning and critical thinking required to interpret real-world data.

• ACARA Content Descriptions
• AC9M9ST01
• AC9M9ST02

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Pair Sort: Histogram Shape Identification

Provide printed histograms of familiar data like test scores or heights. Pairs match each to descriptions of shape (symmetric, skewed right, bimodal). They then justify choices and create one histogram from class data using graphing tools.

What does the shape of a histogram tell us about the distribution of data?

Facilitation Tip

During Pair Sort: Histogram Shape Identification, circulate and ask each pair to explain their bin choices and the shape they see, listening for accurate vocabulary like 'cluster' or 'gap'.

What to look for

Provide students with a small data set and a pre-drawn box plot. Ask them to: 1. Identify any potential outliers shown on the box plot. 2. Calculate the Interquartile Range (IQR). 3. Explain in one sentence how an outlier might affect the mean of this data set.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Small Group: Outlier Investigation Stations

Set up stations with box plots from real Australian datasets (e.g., rainfall, AFL scores). Groups identify outliers, calculate affected measures before and after removal, and discuss validity. Rotate stations and share findings.

How do outliers affect the interpretation of data and statistical measures?

Facilitation Tip

In Outlier Investigation Stations, assign each group a different data set so you can compare varied outlier contexts during the debrief.

What to look for

Display a histogram of student test scores. Ask students to write down two observations about the shape of the distribution (e.g., 'It looks symmetric', 'Most scores are clustered between 70 and 80'). Then, ask them to identify a possible score that might be considered an outlier and explain why.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 20 min · Whole Class

Whole Class: Stem-and-Leaf Plot Challenge

Collect class data on a quick survey (e.g., minutes spent on homework). Display as stem-and-leaf plot on board. Class votes on outliers, redraws plot, and compares measures. Discuss shape implications.

Justify the importance of identifying outliers in a data set.

Facilitation Tip

For the Stem-and-Leaf Plot Challenge, model how to convert a stem-and-leaf plot back into raw numbers to verify accuracy before students attempt their own.

What to look for

Present two different data sets with similar medians but different ranges and outlier presence. Pose the question: 'If you had to choose one data set to represent typical student performance on a recent test, which would you choose and why? Consider the impact of outliers and the overall spread of the data.'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 25 min · Individual

Individual: Data Display Redesign

Give students a messy dataset with outliers. They choose and create two displays (e.g., histogram and box plot), annotate shapes and outliers, then write a conclusion paragraph.

What does the shape of a histogram tell us about the distribution of data?

Facilitation Tip

In Data Display Redesign, review students' drafts early to catch misinterpretations of scale or outlier placement before they finalize their work.

What to look for

Provide students with a small data set and a pre-drawn box plot. Ask them to: 1. Identify any potential outliers shown on the box plot. 2. Calculate the Interquartile Range (IQR). 3. Explain in one sentence how an outlier might affect the mean of this data set.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teachers should balance direct instruction on data display conventions with open-ended exploration so students confront their own misconceptions. Avoid rushing to definitions; instead, let students grapple with messy data first, then refine their language with teacher guidance. Research shows that students learn to interpret shapes and outliers best when they repeatedly compare displays and discuss differences in small groups.

Successful learning looks like students confidently describing data shapes and justifying outlier decisions with evidence. They should move from identifying features to explaining why those features matter for interpreting the data set. Peer discussion and justification are key markers of understanding.

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Watch Out for These Misconceptions

• During Pair Sort: Histogram Shape Identification, watch for students who assume all histograms should look symmetric or bell-shaped.

  Use the physical sorting task to redirect: Have pairs place their histogram next to one that is skewed, then ask them to describe what real-world scenario might create each shape, reinforcing that skewness reveals the data's context.

• During Outlier Investigation Stations, watch for students who automatically remove any outlier without considering its context.

  Provide each station with a scenario card (e.g., 'This data is daily temperatures in a desert town'). Require groups to justify whether the outlier is valid before deciding to keep or remove it, using the scenario to guide their reasoning.

• During Stem-and-Leaf Plot Challenge, watch for students who confuse stem-and-leaf plots with bar graphs or who misread the stems as categories.

  In the challenge, include a step where students convert their stem-and-leaf plot back into a raw list, then compare it to the original data set to verify accuracy and reinforce the plot's structure.

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Methods used in this brief

• Problem-Based Learning