Measures of Central Tendency

Active learning helps students see that measures of central tendency are not just calculations, but tools for making sense of real-world data. By testing different scenarios, students move beyond rote formulas and begin to judge when each measure truly represents the ‘center’ of a data set.

• 9th Grade
• Mathematics
• 3 activities
• 20 min–35 min

Learning Objectives

1. Calculate the mean, median, and mode for a given data set.
2. Analyze the impact of outliers on the mean and median of a data set.
3. Compare and contrast the mean, median, and mode to determine the most appropriate measure of central tendency for various data distributions.
4. Explain how the spread of data provides information not captured by measures of central tendency.

Inquiry Circle

⏱ 30 min·Small Groups

Inquiry Circle: The Outlier Effect

Groups are given a data set of 'salaries' for a small company. They calculate the mean and median. Then, they add a 'CEO salary' that is 10 times larger and recalculate. They must discuss which measure now better represents a typical worker.

Prepare & details

Analyze how outliers affect the mean compared to the median.

Facilitation Tip: During Collaborative Investigation: The Outlier Effect, circulate and listen for students to use phrases like ‘pulled by the extreme value’ when discussing the mean’s sensitivity to outliers.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Which Average Wins?

Provide three scenarios (e.g., shoe sizes in a store, home prices in a neighborhood, test scores). Students work in pairs to decide whether the mean, median, or mode would be most useful for a specific person in that scenario (e.g., the store owner vs. the home buyer).

Prepare & details

Differentiate which measure of center is most appropriate for skewed data distributions.

Facilitation Tip: For Think-Pair-Share: Which Average Wins?, remind pairs to ground their choice in the context first, then justify with calculations.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Simulation Game

⏱ 35 min·Whole Class

Simulation Game: Data Collection Derby

Students perform a quick physical task (like how many paperclips they can chain in 30 seconds). They pool their data as a class and use different measures of center to describe their performance, debating which one is the 'fairest' representation.

Prepare & details

Explain what story the spread of data tells us that the average cannot.

Facilitation Tip: In Simulation: Data Collection Derby, ensure timers are visible so students associate the data-gathering pace with variability in the mean.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Teaching This Topic

Teachers approach this topic by setting up comparisons: students analyze the same data set using mean, median, and mode, then defend which one tells the clearer story. Avoid rushing to definitions; instead, let students experience the ‘why’ first through concrete examples before formalizing language. Research suggests that students grasp the impact of skewness and outliers better when they generate skewed data themselves rather than being handed a pre-made table.

What to Expect

Successful learning shows when students can explain why one average is better than another in context, and when they notice how an outlier or skew can distort the mean. They should also demonstrate the habit of ordering data before finding the median, not just recalling the steps.

Watch Out for These Misconceptions

Common Misconception

During Collaborative Investigation: The Outlier Effect, watch for students to believe the mean is always the best or most ‘mathematical’ average.

What to Teach Instead

During Collaborative Investigation: The Outlier Effect, redirect students by asking them to compare the CEO salary scenario and the rest of the employees, then re-examine which average best represents the ‘typical’ worker.

Common Misconception

During Think-Pair-Share: Which Average Wins?, watch for students forgetting to put the data in order before finding the median.

What to Teach Instead

During Think-Pair-Share: Which Average Wins?, hand each pair a stack of numbered index cards to physically sort before identifying the median, reinforcing the necessity of ordering.

Assessment Ideas

Quick Check

After Collaborative Investigation: The Outlier Effect, give students a small data set, ask them to calculate mean and median, then add an outlier and recalculate. Have them explain in one sentence how the outlier changed each measure.

Discussion Prompt

After Think-Pair-Share: Which Average Wins?, present Scenario B (tech startup salaries) and ask students to share their chosen measure with a partner, using evidence from their calculations.

Exit Ticket

During Simulation: Data Collection Derby, collect each group’s final data set and mean. Ask students to write one sentence comparing their mean to the class’s overall mean and what that difference suggests about variability in their data.

Extensions & Scaffolding

• Challenge students to create a data set where the mode is the most misleading measure, and justify why in two sentences.
• Scaffolding: Provide a partially ordered data set on cards for students to arrange before finding the median.
• Deeper exploration: Have students research and present an example from media or policy where choosing the wrong average misled the public.

Key Vocabulary

Mean	The average of a data set, calculated by summing all values and dividing by the number of values. It is sensitive to extreme values.
Median	The middle value in a data set when the values are arranged in order. It is not affected by outliers.
Mode	The value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode.
Outlier	A data point that is significantly different from other observations in the data set. Outliers can skew the mean.
Skewed Distribution	A data distribution that is not symmetrical, meaning the data tends to cluster more to one side. This affects which measure of center is most representative.