Applications of Statistics

Overview

This lesson applies earlier learning about summarising and comparing data to realistic contexts from media-style tables and graphs. Students will interpret spread measures (range, interquartile range, standard deviation) and decide which are suitable for the situation.

Learning intentions

Students will be able to:

• interpret summary statistics and what they suggest about variability in a real scenario
• compare at least two groups using appropriate measures of spread
• evaluate whether a source’s statistical claims are reasonable given the data summary
• justify their choice of measure of spread using clear mathematical reasoning

Success criteria

Students can:

• state what range, interquartile range (IQR), and standard deviation mean in context
• choose the most suitable spread measure for skewed/outlier-prone data and explain why
• compare groups by referencing numerical spread (not only “it looks bigger”)
• critique a misleading interpretation using evidence from the given table/graph

Curriculum links

• Sub-topic: Summarising and interpreting data — calculate and interpret statistical measures of spread, including range, interquartile range and standard deviation
• Sub-topic: Summarising and interpreting data — investigate inappropriate uses of measures of central tendency and spread in real-world examples
• Sub-topic: Summarising and interpreting data — investigate suitability of measures of central tendency in various real-world contexts (applied here by linking spread choice to context)

Lesson structure (60 minutes)

1. 0–5 min · Hook (media claim). Teacher displays a short “news-style” claim: “Dataset A is more consistent than Dataset B because its standard deviation is smaller.” Students quickly write: “Agree/Not sure/Disagree” and one reason.

2. 5–15 min · Retrieval and key ideas. Teacher leads a brief recap: define range, IQR, and standard deviation using plain language and link each to sensitivity to outliers. Students complete a 3-question mini-check on a single small dataset (e.g., identify which measure would be least affected by one extreme value).

3. 15–30 min · Guided application: interpreting a spread comparison. Teacher provides a table for two groups (e.g., “Commute times” for two transport routes) and one accompanying simple boxplot or summary plot. Students, in pairs then individually, calculate and/or interpret: range, IQR, and standard deviation for each group (depending on what is given, they may compute one measure and interpret others).

4. 30–40 min · Decision task: choose the most suitable measure of spread. Teacher prompts: “Which statistic should the reporter use to support a claim about consistency, and why?” Students write a short justification choosing between IQR and standard deviation, considering outliers and shape of the data (skew/heavy tails).

5. 40–55 min · Critique a misunderstanding (real-world context). Teacher gives a second scenario where the claim is questionable, such as:

• using range to compare “consistency” when one outlier dominates, or
• using standard deviation without checking context where a robust measure is more appropriate. Students identify the issue, then revise the claim into a mathematically supported statement.

6. 55–60 min · Exit ticket. Students answer two prompts:

• “In one sentence, what does IQR tell us about spread?”
• “One sentence: which spread measure would you recommend here and why?”

Resources

• Printed scenario sheets with two datasets (tables and either quartiles/boxplot or summary values)
• Calculator access or built-in calculator on devices
• Graph/boxplot visuals prepared in advance (printed or on screen)
• Student mini-check worksheet (3 short items)
• Exit ticket slips or online form
• Marker/board space for modelling sample reasoning

Assessment

• Formative: teacher circulates during the guided calculations, checking that students correctly interpret what each spread measure indicates
• Formative: review students’ justifications for using the most suitable spread measure (focus on reasoning, not just the number)
• Summative-in-mini: exit ticket to verify understanding of IQR and appropriate measure selection

Differentiation

• Support: provide sentence starters for justifications (e.g., “IQR is suitable here because…”, “A smaller standard deviation suggests…”); offer a worked example of one calculation step
• Support: highlight outliers on the provided table/plot and explicitly ask which measure is robust to outliers
• Extension: challenge students to propose an alternative, more accurate claim using a different spread measure and explain how the wording changes
• EAL/SEN: keep scenarios visually structured (clear labels for Group A/B, “reporter claim” box, “data summary” box) and allow oral explanation before writing