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.

• Year 9
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Analyze the shape of histograms (e.g., symmetric, skewed left, skewed right) to describe the distribution of a data set.
2. Compare and contrast data presented in histograms, box plots, and stem-and-leaf plots to identify similarities and differences in data spread and central tendency.
3. Identify potential outliers in box plots and stem-and-leaf plots using established rules, such as the 1.5 IQR rule.
4. Evaluate the impact of identified outliers on measures of central tendency (mean, median) and spread (range, IQR) for a given data set.
5. Justify the significance of identifying and handling outliers when drawing conclusions from statistical data.

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.

Prepare & details

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'.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Pair Sort: Histogram Shape Identification, distribute a data set and a blank histogram template. Ask students to sketch a histogram, label its shape (e.g., skewed left), and write one sentence explaining what the shape suggests about the data's context.

Quick Check

During Outlier Investigation Stations, listen for groups that correctly apply the 1.5*IQR rule and justify their outlier decisions with the data set's context. Note which groups rely solely on rules versus those who connect outliers to real-world meaning.

Discussion Prompt

After Data Display Redesign, display two student histograms side by side with different bin widths or outlier treatments. Ask the class to discuss which display better represents the data and why, focusing on how design choices impact interpretation.

Extensions & Scaffolding

• Challenge: Provide a data set with a known outlier and ask students to redesign the histogram with and without the outlier, analyzing how each version changes the shape and summary statistics.
• Scaffolding: Give students a partially completed box plot template with key values filled in to reduce cognitive load while they practice identifying outliers using the 1.5*IQR rule.
• Deeper: Introduce a second data set from a different context (e.g., sports vs. environmental) with similar outliers and ask students to write a paragraph comparing how outliers influence interpretation in each field.

Key Vocabulary

Outlier	A data point that is significantly different from other observations in a data set. Outliers can skew statistical results and require careful consideration.
Histogram	A bar graph representing the frequency distribution of numerical data. The bars represent ranges of data, and their height indicates the frequency within that range.
Box Plot (Box and Whisker Plot)	A standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It visually shows the spread and potential outliers.
Stem-and-Leaf Plot	A method of organizing data to show the shape of the distribution. It separates each data point into a 'stem' (the leading digit or digits) and a 'leaf' (the last digit).
Skewness	A measure of the asymmetry of a probability distribution of a real-valued random variable about its mean. A distribution can be skewed left, skewed right, or be symmetric.