Statistical Applications

Overview

In this lesson (Lesson 8 of 9), students apply earlier skills to interpret real data presented in tables and graphs, then summarise and compare data using spread measures. They will work through a practical scenario, calculate appropriate statistics (including range, interquartile range and standard deviation), and justify which measure best supports a conclusion.

Learning intentions

• Students will interpret tables and graphs to extract key information about a dataset.
• Students will calculate and compare measures of spread: range, interquartile range (IQR) and standard deviation.
• Students will decide which summary statistic best supports a conclusion in a real-world context.
• Students will communicate results using correct statistical language (variation, spread, typicality, outliers).

Success criteria

• I can correctly identify the median and quartiles from a distribution (including from a box plot).
• I can calculate range and IQR, and explain what each measure tells me about spread.
• I can interpret standard deviation as the average magnitude of deviation from the mean and compare results across scenarios.
• I can write a short conclusion that links the statistics to the context.

Curriculum links

• Summarising and comparing data: calculate and interpret statistical measures of spread, including range, interquartile range and standard deviation (complex).
• Summarising and interpreting data: use appropriate statistical measures to compare datasets.
• Representing data: interpret displays such as tables and graphs to draw meaning from data representations.

Lesson structure (60 minutes)

1. 0–5 min · Warm-up prompt. Teacher displays two short summaries of datasets (e.g., “Dataset A: values clustered” vs “Dataset B: values vary widely”) without calculations, then asks: “Which measure of spread would you choose first, and why?” Students vote and justify briefly in pairs.

2. 5–15 min · Model: reading spread from visuals. Teacher revisits how to read data displays: from a table (find min/max and quartiles via ordered values or provided quartiles) and from a box plot (median, Q1, Q3). Teacher models how range and IQR connect to outliers and middle spread, using one worked example step-by-step. Students follow and complete two “spot the quartile” checks.

3. 15–35 min · Guided practice: practical scenario. Teacher provides a scenario: comparing test results across two classes or two teaching strategies. Each group receives a small dataset table (e.g., 12–20 values each) and a summary box plot image or quartile values (printed). Teacher explicitly walks students through:

• finding min/max for range,
• determining Q1 and Q3 for IQR,
• computing standard deviation using technology (calculator/statistics mode) or teacher-provided formula steps. Students record calculations in a structured template and check reasonableness (e.g., IQR should reflect central spread; standard deviation should be larger when values are more dispersed).

4. 35–50 min · Decision-making: compare and justify. Teacher asks students to answer: “Which option should be recommended, and what does the variability evidence show?” Students compare the two datasets using at least two measures (range and IQR, plus standard deviation) and explain:

• whether spread is driven by outliers (range vs IQR),
• whether both datasets have similar medians but different consistency (IQR and standard deviation),
• which measure is most informative for the decision context. Teacher circulates, prompting with sentence starters: “IQR suggests…”, “Standard deviation indicates…”, “Because…”.

5. 50–58 min · Exit ticket (quick check). Teacher gives one mini-dataset and asks for: (a) range, (b) IQR given Q1 and Q3, (c) a short interpretation sentence choosing the best spread measure for a stated reason.

6. 58–60 min · Whole-class debrief. Teacher collects two exit-ticket interpretations and highlights common correct reasoning and one typical misconception (e.g., mixing up IQR with range; misinterpreting standard deviation direction).

Resources

• Printed dataset handouts for two scenarios (tables of values) and/or box plot quartile information
• Box plot reference sheet (labels: min, Q1, median, Q3, max)
• Calculator or device with statistics capability
• Student recording template: “Range / IQR / Standard deviation / Conclusion”
• Exit ticket slips
• Board/slide with worked example steps (range, IQR, standard deviation interpretation)

Assessment

• Formative: teacher checks during guided practice for correct extraction of min/max, Q1/Q3, and correct substitution into calculations.
• Formative: listen for accurate interpretation statements using correct terms (spread, outliers, consistency).
• Exit ticket: accuracy of range and IQR plus a written justification linking the statistic to the context.

Differentiation

• Support: provide a partially completed calculation table and sentence starters for conclusions (“The IQR tells us about the spread of the middle 50% of results.”).
• Support: allow use of technology for standard deviation, with teacher confirming interpretation rather than requiring manual computation.
• Extension: for students who finish early, ask them to rank three datasets by “central consistency” using IQR and standard deviation, then justify why range may be misleading if outliers exist.
• EAL/SEN: reduce cognitive load by supplying quartiles directly where possible; provide a one-page glossary of statistical terms and common interpretation phrases.