Data Into Evidence

Overview

Students conduct a short statistical investigation using the PPDAC cycle: Problem, Plan, Data, Analysis and Conclusion. Working in groups of four, they collect class data about preferred chocolate bars, organise it in a tally and frequency table, construct a bar graph, and make an evidence-based conclusion.

Learning intentions

• WALT formulate a measurable statistical question and prediction.
• WALT collect and represent categorical data accurately using a tally, frequency table and bar graph.
• WALT interpret data using frequency, mode and percentages.
• WALT communicate a conclusion supported by numerical evidence and identify limitations in an investigation.

Success criteria

• I can write a clear question with a defined population and categories.
• I can record data accurately and check that my frequencies match the total responses.
• I can draw a correctly labelled bar graph with an even scale, equal-width bars and spaces between bars.
• I can make a conclusion using data and explain one limitation or possible source of bias.

Curriculum links

• Mathematics and Statistics — statistical investigations, data collection, representation and interpretation.
• Mathematics and Statistics — using mathematical reasoning to make sense of variation and evidence.
• Mathsteasers — higher-order thinking and challenge through non-routine questions.
• Mathematical and statistical thinking — communicating findings, justifying decisions and evaluating the quality of data.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Teacher displays a deliberately misleading bar graph with a shortened vertical axis using the hook and graph critique slides and asks, “Can a graph be technically correct but give a misleading impression?” Students think-pair-share, identify features of a trustworthy graph, and recall tally, frequency, mode and categorical data.

2. 7–15 min · Model the PPDAC cycle. Teacher introduces the five stages on the PPDAC teaching slides and models the question, “Which chocolate bar is most popular in our class?” Explain that the independent variable is chocolate-bar category and the dependent variable is the frequency counted. Students help improve the question by specifying the population, make a prediction, and suggest fair ways to collect responses.

3. 15–22 min · Plan the investigation. Teacher places students in five groups of four and distributes the Statistical Investigation Planning Frame. Guide groups to agree on categories, a consistent question, the population surveyed and how responses will be recorded. Students complete the Problem and Plan sections, including a prediction and one consideration about sample size or bias.

4. 22–32 min · Collect and check data. Teacher displays the agreed categories and instructions using the data-collection instructions; each group surveys four other students, recording one response per person with tally marks. Students combine their group results into a class tally and frequency table on the bar graph investigation worksheet, then check that the total frequency equals 20.

5. 32–47 min · Represent and analyse. Teacher models a suitable scale and the essential graphing checklist on the graph construction and analysis slides. Students construct a bar graph with a descriptive title, category labels, frequency axis beginning at zero, even intervals, equal-width bars and spaces between bars. They answer the worksheet questions: identify the mode, compare the most and least popular categories, and calculate at least two percentages using frequency ÷ 20 × 100.

6. 47–55 min · Conclusions and critique. Teacher prompts groups to use their data to answer the original question and discuss whether the prediction was supported. Students write a short conclusion on the worksheet including the winner, numerical evidence, prediction comparison and one limitation, such as small sample size, limited population, timing or response bias. Invite two groups to share and compare conclusions.

7. 55–60 min · Plenary and exit check. Teacher uses the plenary and exit-question slide to revisit the PPDAC cycle. Students complete the final worksheet prompt: “How might the result change if 200 students from the whole school were surveyed?” and hand in their graph and conclusion.

Resources

• the complete PPDAC investigation slide deck
• the bar graph investigation worksheet
• the Statistical Investigation Planning Frame
• Board or shared digital display
• Rulers, pencils and coloured pencils
• Calculators or calculator applications
• Group data-recording sheets or exercise books

Assessment

• Listen during planning for measurable questions, clear populations, appropriate categories and awareness of fairness or bias.
• Check tally-to-frequency totals, graph conventions, correct identification of the mode and percentage calculations while circulating.
• Collect the worksheet as an exit assessment, looking for a conclusion that answers the question and uses numerical evidence, plus a relevant limitation.

Differentiation

• Support students with a completed example of one tally row, a graph checklist, a pre-drawn axis and sentence starters such as “The most common category was ___, with ___ responses” and “This result may be affected by ___.”
• Provide dyslexia-friendly copies: clear sans-serif font, generous spacing, uncluttered layout, short numbered instructions and high-contrast graph lines. Read instructions aloud and allow speech-to-text or oral recording of the conclusion.
• Pair students strategically and assign roles such as questioner, recorder, checker and graph designer. Permit calculators and a digital graphing tool where fine-motor or processing needs make drawing a graph a barrier.
• Extension: students calculate percentages for every category, compare the class sample with a hypothetical whole-school sample, and explain how sample size, representativeness or bias could affect the reliability of the conclusion.