Basics of Data Analysis

Overview

In this 60-minute lesson (lesson 7 of 9), students learn how to collect and represent data for a single variable, then calculate and interpret mean, median, mode, and range. The lesson also revisits probability language and how probability ideas connect to variability in data.

Learning intentions

• Students will be able to select an appropriate way to collect data for a single numerical variable.
• Students will be able to represent data in an ordered list and summary table suitable for calculations.
• Students will be able to calculate mean, median, mode, and range from a dataset.
• Students will be able to interpret what each measure suggests about the data and identify limitations (e.g., outliers).
• Students will be able to connect probability concepts (likelihood, expectation) to what data might look like.

Success criteria

• I can calculate mean, median, mode, and range correctly from an ordered dataset.
• I can explain how the median and range respond differently to outliers.
• I can state what the measures mean in context (not just give numbers).
• I can use probability terms to describe why outcomes vary and why repeats may give different results.

Curriculum links

• QCAA General Mathematics — Unit 2 / Topic 4: Univariate data analysis 1: Understand and calculate mean, median, mode, range, and interquartile range (IQR) with and without technology; be aware of limitations.
• QCAA General Mathematics — Unit 2 / Topic 4: Univariate data analysis 1: Use statistics as measures of centre and spread; understand their limitations.
• QCAA Essential Mathematics — Unit 4 / Topic 2: Summarising and interpreting data: Calculate and interpret median and mean from a dataset of values.
• QCAA Essential Mathematics — Unit 4 / Topic 2: Summarising and comparing data: Calculate and interpret spread, including range and interquartile range (complex).

Lesson structure (60 minutes)

1. 0–5 min · Starter: probability-to-data prompt. Teacher displays two statements: “A fair spinner is more likely to show 3 than 1” and “Two students may get different results when both roll the same die repeatedly.” Students decide which statement is correct and justify using probability language (likely/impossible/equally likely/expected).

2. 5–15 min · Direct teach: collecting and representing univariate data. Teacher introduces the class task: collect a single numerical variable from a small random sample (e.g., number of steps taken to walk 5 metres, time in seconds for 3 ball taps, or number of questions answered correctly in 2 minutes—teacher chooses one manageable option). Students follow teacher modelling: record values, organise into a list, sort, and create a simple frequency table if repeats occur.

3. 15–25 min · Model calculations: centre measures. Teacher uses a worked example dataset (from the class collection or a prepared set) to show calculations of mean, median, and mode. Students mirror the steps on their own copy: compute mean by total divided by count; find median from the ordered list (handle odd/even sizes); identify mode from the most frequent value (or “no mode” if all values are equally frequent).

4. 25–33 min · Guided practice: spread measure (range). Teacher explains range as maximum minus minimum and demonstrates with the same dataset. Students compute range, then answer: “Does the range tell the whole story?” Students discuss in pairs (one sentence each).

5. 33–45 min · Independent task: full summary and interpretation. Teacher provides a dataset of 12–16 values (or uses the class dataset) plus a response sheet with four prompts: calculate mean, median, mode, range; compare mean vs median; interpret mode; and write one limitation statement. Students complete calculations and write short interpretations in context (e.g., “Median is a better measure if there is an extreme result…”).

6. 45–55 min · Technology check and reasoning: sanity testing. Teacher allows calculators/spreadsheets only for checking arithmetic (mean and median should be reasoned from the ordered data). Students verify at least one calculation and then do a quick “reasonableness check”: identify if an outlier could shift the mean, and whether range reflects extreme values.

7. 55–60 min · Exit ticket: measure selection + probability link. Teacher asks: “Given this scenario, which measure(s) would be most useful (mean or median; range or IQR if introduced later), and why?” Include one probability sentence such as “Because results vary, we expect…” Students submit a short response with calculations shown or clearly referenced.

Resources

• Prepared dataset(s) for the dataset task (printed and/or on board)
• Student response sheet template with rows for mean, median, mode, range and interpretation prompts
• Calculator(s) and/or classroom device with spreadsheet capability for checking
• Whiteboard/marker and visual example of sorted data
• Optional: spinner/die or timer for the initial collection context (only if teacher chooses that option)
• Checklist for success criteria (teacher-made)

Assessment

• Formative: teacher circulates during guided and independent practice, checking median and mode decisions (common error points).
• Formative: pair discussion at 25–33 minutes—listen for correct range reasoning and limitations language.
• Exit ticket: evaluate whether students can interpret measures and link probability ideas to variability using correct mathematical language.

Differentiation

• Support: provide sentence starters for interpretation (e.g., “The median is…” “This is useful because…” “An outlier could…” “Range shows…”). Supply a partially ordered list if students struggle to sort.
• Support for median: provide a clear algorithm reminder: order data, locate the middle value(s), average if needed.
• Extension: ask students to justify why mean and median may differ using a specific data value (e.g., the smallest or largest result).
• EAL/SEN considerations: allow oral explanation before written work; highlight key terms (centre, spread, ordered, maximum, minimum, most frequent, likely, equally likely) and keep them consistent across the lesson.