Year level: 8

Strand: Statistics

Lesson length: 55 mins

Students will plan and conduct a statistical investigation to find the average height of students at their school. Students analyse and report on the distribution of their data for the ‘whole’ school drawing conclusions with respect to different sampling techniques and whether methods chosen were fair and considered.

This lesson is one of a series of lessons that can be used to assist students to plan and conduct a statistical investigation.

### Achievement standard

Students conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range.

### Content descriptions

Students learn to investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques. AC9M8ST01

Students learn to compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation. AC9M8ST03

They plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty. AC9M8ST04

### General capabilities

Numeracy

• Interpreting and representing data (Level 7)

Digital Literacy

Ethical understanding

• Exploring ethical issues (Level 5)

Critical and creative thinking

• Draw conclusions and provide reasons (Level 5)
• Develop questions (Level 5)
• Identifying, processing and evaluating information (Level 5)
• Consider alternatives (Level 5)

The following assessment opportunities are suggested for this 3-part investigation.

Students work in groups to collate data and record their findings in a report to be assessed. Distribute the assessment rubric for guidance.

Students can present their findings to the class if time allows.

It is expected that students have:

• a basic understanding of statistics and data sampling
• familiarity with terms: sampling, representative, random choice, population, survey.

Some students may:

• use sampling methods that affect accuracy and demonstrate underestimating and bias
• think that statistical investigation requires data from the entire population
• believe that statistical investigations always have a clear answer
• have difficulty creating graphs and calculating summary statistics using technology.

To address the areas of challenge, the following suggestions are below. Teachers can:

• emphasise the importance of choosing appropriate sampling methods, use examples to demonstrate the impact on accuracy, highlight pros and cons of different methods, and engage students in comparing outcomes with different sampling methods
• explain the difference between population and sample, highlight the impracticality of collecting data from the entire population and provide examples of investigations using samples, for example, market research versus census
• highlight the uncertainty and variability in statistical investigations, explain that conclusions are based on probabilities and can vary with samples, engage students in analysing results with consideration for uncertainty
• use group structures to leverage a wider range of skills and knowledge, source easy guidance videos, use an excel template with pre-coded stats and graphs.

## What you need:

• Lesson plan (Word)

• Teacher's slides (PowerPoint)

• Are you average template (Excel)

• Teacher's notes and examples (Word)

• Assessment rubric (Word)

• Digital devices (tablets or computers)

• Collated student data