Mathematics · Year 10

Active learning ideas

Measures of Central Tendency

Active learning works because constructing cumulative frequency graphs and box plots requires spatial reasoning and pattern recognition that static examples cannot provide. When students physically plot points or measure class boundaries, they develop an intuitive sense of how data accumulates and spreads, which is difficult to grasp from formulas alone.

• National Curriculum Attainment Targets
• GCSE: Mathematics - Statistics

• 15–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 45 min · Small Groups

Inquiry Circle: Comparing Datasets

Groups are given two sets of data (e.g., test scores from two different classes). They must calculate the cumulative frequencies, draw the graphs, and create box plots to decide which class performed 'better' and why.

Compare the strengths and weaknesses of mean, median, and mode as measures of central tendency.

Facilitation Tip

During the Collaborative Investigation, circulate and ask groups to explain how their cumulative frequency graph changes as they add each new interval.

What to look for

Present students with two small datasets: one with a clear outlier, and one without. Ask them to calculate the mean, median, and mode for both. Then, ask: 'Which measure best represents the 'typical' value in each dataset, and why?'

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

Activity 02

• Gallery Walk
• 25 min · Pairs

Gallery Walk: Spot the Outlier

Box plots are displayed around the room, some with deliberate errors or extreme outliers. Students move in pairs to identify the outliers using the 1.5 x IQR rule and discuss whether they should be kept or removed from the data.

Evaluate which measure of central tendency is most appropriate for a given dataset.

Facilitation Tip

For the Gallery Walk, place a large copy of each box plot on the wall so students can compare their own plots to the correct versions during the discussion.

What to look for

Provide students with a simple frequency table showing the number of hours students spent on homework last week. Ask them to: 1. Calculate the mean, median, and mode. 2. State which measure they think is most appropriate to describe the typical homework time and briefly justify their answer.

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

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Skewness and Spread

Students are shown three different box plots representing different distributions. They must individually describe the 'story' the data tells (e.g., 'most people scored high but a few did very poorly') before sharing their interpretation with a partner.

Explain how outliers can affect different measures of central tendency.

Facilitation Tip

In the Think-Pair-Share, provide a dataset with a clear skew and ask students to estimate the median and quartiles before calculating, to build intuition.

What to look for

Pose the question: 'Imagine you are analyzing the salaries of employees at a company. Would you prefer to report the mean salary or the median salary? Explain your reasoning, considering the potential impact of a CEO's very high salary.'

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

A few notes on teaching this unit

Teachers should model the precise plotting of cumulative frequency at upper class boundaries, not midpoints, to avoid the common misconception. Use real-world data sets that students can relate to, such as test scores or sports times, to keep engagement high. Avoid rushing to formulas; let students discover relationships between the median, quartiles, and box plot whiskers through guided construction.

Successful learning looks like students accurately plotting cumulative frequency at upper class boundaries, correctly identifying quartiles from their graphs, and constructing box plots that show the spread and skew of datasets. They should confidently explain why the median or IQR is more representative than the mean in skewed distributions.

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Watch Out for These Misconceptions

• During Collaborative Investigation, watch for students plotting cumulative frequency at midpoints instead of upper class boundaries.

  Ask students to trace the step-by-step accumulation of frequencies and point out that the cumulative total 'up to' a boundary includes all data before it, so the point must align with the upper class limit.

• During Gallery Walk, watch for students interpreting longer whiskers as larger frequencies within that quartile.

  Have students measure the length of each section on their box plot and confirm that each quartile always represents 25% of the data, regardless of the whisker length.

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Methods used in this brief

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