Centre and Spread

Overview

This 60-minute lesson is lesson 3 of 19 in the Year 9 Maths 2026 Plan. Students build on prior work with organising and representing data by calculating and interpreting measures of centre and spread, then examining how an outlier changes a data summary and its visual representation.

Learning intentions

Students will:

• Calculate the mean, median, mode, range, quartiles and interquartile range for suitable datasets.
• Interpret numerical summaries alongside dot plots and box plots.
• Explain which measures are appropriate for different distributions.
• Investigate and communicate the effect of an outlier.

Success criteria

• I can accurately calculate and show my method for measures of centre and spread.
• I can use a dot plot or box plot to support my interpretation.
• I can explain how an outlier affects the mean, median, range and interquartile range.
• I can justify which summary measures best describe a dataset.

Curriculum links

• Mathematics and Statistics: statistical investigations, data distributions, and interpreting statistical information.
• Use summary statistics and data displays to communicate features of a distribution, including centre, spread and unusual values.
• Develop the mathematical processes of reasoning, representing, communicating and evaluating conclusions.
• Mathsteasers: challenge advanced learners through higher-order questions and relevant, seamless connections to mathematical content.

Lesson structure (60 minutes)

1. 0–7 min · Human-number-line hook. Teacher displays the data set 4, 5, 5, 6, 7, 8, 9 and asks, “What single number could represent this group, and how could we describe how spread out it is?” Open with the provocative hook and learning intentions and give seven students data cards to arrange physically on a number line. Students position themselves, identify the median and mode informally, and discuss what a “typical” value might mean.

2. 7–18 min · Direct teaching and modelling. Teacher uses the worked-example slides to model ordering data, finding mean, median, mode, range, lower and upper quartiles, and interquartile range; explicitly distinguish the median from the mean and demonstrate a consistent quartile method. Students copy one worked example into the centre-and-spread practice worksheet and check each calculation with a partner. Emphasise that the mean is sensitive to extreme values, while the median and quartiles are generally more resistant.

3. 18–32 min · Paired calculation investigation. Teacher distributes the worksheet and sets pairs three small datasets, including one with repeated values and one containing an outlier. Students calculate the measures, record organised working, and use calculators to verify their results. Pause for hinge questions from the calculation-check slides, such as “Which measure must be found after ordering the data?” and “Which statistic changes most when 100 is added to 4, 5, 5, 6 and 7?” Students hold up answer cards or explain their choice before continuing.

4. 32–43 min · Outlier experiment. Teacher asks pairs to add an extreme value to a shared dataset and complete the before-and-after table on the worksheet. Students compare the mean, median, mode, range and interquartile range, then write two sentences explaining which measures changed substantially and why. Invite selected pairs to present contrasting examples, including an outlier that does and does not change the mode.

5. 43–53 min · Displays and interpretation. Teacher shows a dot plot and corresponding box plot in the representation and discussion slides. Students connect the minimum, lower quartile, median, upper quartile and maximum to the box plot, and describe the distribution using centre, spread and possible outliers. Ask: “Would you report the mean or median for this distribution? What evidence supports your choice?” Students annotate the final worksheet question with a sentence using “because”.

6. 53–60 min · Individual summary and review. Teacher displays the plenary and exit-task slide and asks students to complete the final individual summary task without partner support: “For a dataset with one very large outlier, explain how the mean, median, range and IQR are affected, and identify the most useful measure of centre.” Students hand in their response as they leave and share one measure they can now calculate confidently.

Resources

• the complete centre-and-spread teaching deck
• the centre-and-spread practice worksheet
• Teacher-prepared ordered data cards for the human-number-line demonstration
• Calculators
• Statistical vocabulary cards
• Whiteboard and pens
• Optional spreadsheet with datasets and formula support
• Answer key or teacher calculation notes

Assessment

• Use hinge questions during modelling and paired work to identify misconceptions about ordering data, quartile positions and the effect of outliers.
• Listen for accurate statistical language, particularly the difference between “the mean increases” and “the data are more spread out”.
• Collect the individual summary task and check calculation accuracy, explanation of outlier effects, and justification of the preferred measure.

Differentiation

• Support students with ordered data cards, a step-by-step calculation guide, colour-coded positions for quartiles, calculators and a completed example showing each line of working.
• Provide a vocabulary bank with mean, median, mode, range, quartile, IQR, outlier, centre and spread; allow students to rehearse explanations orally before writing.
• Pair students strategically and provide a reduced dataset with fewer values where working-memory or processing needs make the full task inaccessible.
• Extend confident students with reverse problems: construct two different datasets with the same median and range, or create a dataset with specified mean, median and an outlier, then justify whether the summary is plausible.