Data Dispersion Insights

I am aiming to make two lesson plans, below you will find the rough outline for what i would like to achieve in each;

Lesson Plan 1: Ask students if they know what the definition of an outlier is. Show them the formal definition (Q1/Q3 -/+ IQR x 1.5), go through a heavily guided example question with students. Then apply this knowledge to finding the whole 5-number summary of a dataset including the outliers, demo/work through one with the class, get students to attempt one alone. Then introduce standard deviation. Identifying that it is a measure of spread in a dataset. Show students the formula for calculating SD, give students a question regarding the usage of SD when commenting on an entire dataset (Eagles Vs Monsters example). Then move into and demonstrate the ‘steps to find SD’, notably when doing it by hand. Show students an extended frequency table, get students to attempt to populate it and then show how it can be used to find SD. Then have students attempt some themselves Lesson Plan 2: Remind students of SD formula, comment on how doing it by hand was tedious. Hand out sheet which contains the calculator instructions. Modell the process to the class using an emulator then assign questions for the students to practice SD solutions using calculators.

Overview

This 60-minute lesson is designed for Year 10 Mathematics students in New South Wales (NSW), focusing on statistical concepts of outliers, five-number summary, and standard deviation, aligned closely with the NSW Mathematics Curriculum. It emphasises conceptual understanding, guided practice, and individual application appropriate for 15-16 year olds, with a class size of 24 students.

Curriculum Links

NSW Mathematics Curriculum - Years 9 and 10, focusing on:
- "Compare the distribution of continuous numerical data using various displays, and discuss distributions in terms of centre, spread, shape and outliers"
- "Plan and conduct statistical investigations involving bivariate data" (applies specifically to understanding data distributions)
- "Describe features of distributions including outliers and measures of spread"
This lesson supports the achievement standard of students being able to "compare the variation in distributions", meaningful for statistics and data analysis.

Lesson Objectives

Students will be able to:

Define outliers using the interquartile range (IQR) method including the formula ( \text{Outlier} < Q1 - 1.5 \times IQR ) or ( \text{Outlier} > Q3 + 1.5 \times IQR ).
Calculate the five-number summary (minimum, Q1, median, Q3, maximum) including identification of outliers.
Understand and apply the concept of standard deviation (SD) as a measure of spread.
Manually compute SD step-by-step for given datasets.
Interpret and explain the meaning of SD when comparing datasets.
Use frequency tables (extended) to calculate SD.
Build foundation skills for using calculators for SD (to be expanded in the next lesson).

Resources Required

Whiteboard / projector and markers
Student worksheets with example datasets for five-number summary and SD calculations
Calculators (scientific or graphics for next lesson)
Frequency table templates
Interactive tools or emulator for calculator (optional for demo)

Lesson Breakdown

Time	Activity	Details and Guidance
0 - 5 min	Introduction and Engagement	Begin by asking students: "What is an outlier? Can anyone define it or give an example from everyday data?" Allow brief sharing. Introduce formal outlier definition with the IQR rule on the board. Use simple language: "Outliers are data points that are far away from the middle of the data."
5 - 20 min	Guided Example: Outliers and Five-Number Summary	Present a clear, stepwise example dataset on board/projector. Show how to: (1) order data (2) find quartiles Q1, median, Q3 (3) calculate IQR (4) apply outlier test formula. Collaborate with students to identify outliers and five-number summary. Highlight how outliers fit into this summary.
20 - 30 min	Individual Task: Five-Number Summary & Outliers	Hand out worksheet with different dataset. Task students to find the five-number summary and identify any outliers independently. Teacher circulates, gives support, clarifies misconceptions.
30 - 35 min	Introduction to Standard Deviation (SD)	Explain SD concept: "It measures how data spread out around the mean." Give real-life relevance (example: comparing Eagles' and Monsters' scores). Show the SD formula on board. Stress SD as a spread measure complementing range and IQR.
35 - 45 min	Step-by-Step Manual SD Calculation	Demonstrate how to calculate SD by hand using a small dataset: (1) find mean, (2) find each deviation, (3) square deviations, (4) average squares, (5) square root result. Write steps clearly. Use one student volunteer to do part of calculation.
45 - 50 min	Frequency Table for SD	Show an extended frequency table with grouped data. Explain how frequency affects calculations (multiply squared deviations by frequencies). Assign a simple example for students to populate and use to calculate SD partially.
50 - 58 min	Student Practice: Frequency Tables & SD	Students complete SD calculation from given frequency tables individually or in pairs. Encourage checking answers with peers.
58 - 60 min	Summary and Next Steps	Recap key points: outliers, five-number summary, what SD tells us. Mention that next lesson will cover calculator use for SD. Collect worksheet responses.

Assessment and Feedback

Formative Assessment through:
- Questioning during guided practice
- Worksheet completion for five-number summary and SD calculation
- Observation of student engagement and answering during manual SD steps
Informal peer discussion during frequency table tasks enables immediate feedback.
Teacher notes to identify students requiring further support.

Differentiation and Engagement Tips

Provide step checklists on worksheets for students needing extra support.
Use concrete examples relevant to students’ interests (e.g., sports statistics Eagles vs Monsters).
Challenge advanced students with larger datasets or ask them to justify why or when outliers may be excluded in analysis.
Incorporate visual aids like box plots to illustrate five-number summaries and outliers visually.

Homework Suggestion (Optional)

Assign a dataset with a variety of values for students to calculate the five-number summary, check for outliers, and calculate SD manually.
Ask reflective questions on how outliers and SD help in understanding the dataset spread.

With this lesson plan, teachers can confidently deliver comprehensive content on data dispersion measures as required by the NSW curriculum, supporting students to achieve both conceptual understanding and procedural skills in statistics.

Teaching Instructions