Understanding Variability

Overview

In this lesson, students explore variability as “how spread out” data are and how that affects comparisons. They will create and interpret stem-and-leaf plots using software or teacher-made templates, then describe centre and spread using mean, median, mode, range, and outliers.

Learning intentions

Students will:

• WALT understand variability in data and what it indicates about a distribution.
• WALT describe and compare distributions using shape, centre and spread.
• WALT identify outliers and calculate range, median, mean and mode from numerical data.

Success criteria

Students can:

• explain variability as differences in how values are spread out.
• describe whether a distribution is more “clustered” or “spread out” using correct terms.
• calculate range, median, mean and mode and state which one best represents “typical” for the data.
• point out likely outliers and explain how they affect spread and averages.

Curriculum links

• AC9M7ST02: create different numerical data displays including stem-and-leaf plots (using software where appropriate) and describe/compare distribution with shape, centre and spread including outliers; determine range, median, mean and mode.
• AC9M7ST01: acquire/calculates range, median, mean and mode for discrete and continuous variables and justify which measures of centre best suit the distribution.
• AC9M7ST03: analyse and interpret distributions and report findings in terms of shape and summary statistics, as part of a statistical investigation.

Lesson structure (60 minutes)

1. 0–6 min · Quick hook (discussion). Teacher shows two short “class data” scenarios (e.g., shoe sizes: mostly similar vs. widely different) and asks: “Which dataset is more variable and how can you tell without calculating?” Students turn-and-talk, then share one reason.

2. 6–15 min · Direct teach with a visual model. Teacher draws two dot-clusters or a simple stem-and-leaf skeleton on the board: Dataset A is tightly clustered, Dataset B is more spread with one unusual value. Teacher introduces/recaps: variability, outlier, range, and how mean vs median can differ with skew/outliers. Students complete a 3-question “spot the variability” check (thumbs up/down + brief written reason).

Success criteria for this step: identify “spread” and describe it using words like clustered, spread out, outlier, and skew.

3. 15–25 min · Create stem-and-leaf plots. Teacher distributes a data set for heights (cm) or reaction time (ms) with 20–30 values (age-appropriate). Students enter data into software (or teacher provides a stem-and-leaf template) and produce an ordered stem-and-leaf plot. Teacher circulates to check correct stems and ordered leaves. Students confirm the plot represents the data by counting frequencies in at least one stem.

4. 25–38 min · Calculate summary statistics (small groups). Groups calculate range, median, mean, and mode from the same data set. Teacher provides an allowable method sheet (e.g., how to find median from ordered values; how to interpret mode from the plot). Each group identifies:

• the most typical value (mode and/or median)
• the main sign of variability (range, spread in stems, and/or outlier)
• whether an outlier exists and how it might influence mean

Teacher prompts: “Where is the centre located in the plot? Are most values near it?”

Success criteria for this step: correct calculations and an explanation tied to the display.

5. 38–50 min · Compare two distributions (variability focus). Teacher reveals Dataset B (same “topic”, different spread). Students use the already-produced display for A and quickly generate a mini-display for B (split stems or a second stem-and-leaf on the worksheet). Whole class compares:

• which dataset has greater variability
• how shape affects centre (median vs mean) and spread
• whether outliers change conclusions

Students record a 4-sentence comparison:

• “Both datasets show…”
• “Dataset A is more/less variable because…”
• “The median is…, the mean is…”
• “Outliers: yes/no; they affect variability by…”

6. 50–57 min · Class discussion: “So what?” Teacher leads a conversation: “If you only reported the mean, what information could you miss? How would variability change a real-life decision?” Students answer with sentence starters and one evidence reference to their stem-and-leaf plots.

7. 57–60 min · Exit ticket (individual). Students answer:

• Define variability in one sentence.
• Circle the outlier (if present) on a provided small stem-and-leaf.
• Choose which measure best represents “typical” (mean or median) and justify in 1 line.

Resources

• Laptops or tablets with simple spreadsheet/stem-and-leaf tool (or offline software)
• Prepared stem-and-leaf templates (A4) with stems pre-written
• Data cards for two datasets (A and B), 20–30 values each
• Calculation sheets: median from ordered list; mean formula reminder; range/mode notes
• Whiteboard/markers and projector
• Coloured pencils/highlighters to mark outliers and centre

Assessment

• Formative: teacher observation of stem-and-leaf accuracy (correct stems, leaves ordered, frequency counts)
• Formative: group discussion prompts during statistics calculations (range/median/mean/mode and variability explanation)
• Summative/quick check: exit ticket—variability definition, outlier identification, and justification of mean vs median

Differentiation

• Support: sentence starters for comparisons (e.g., “More variable means…”, “I know this because…”, “The outlier affects…”); provide partially completed stem-and-leaf for students who need reduced workload.
• Support for dyslexia: dyslexia-friendly reading options include larger font data sheets, colour-coded columns (stems/leaves), and access to read-aloud (teacher reads the instructions/data aloud). Allow oral responses for parts of the exit ticket.
• Extension: students choose a real-life context (sport scores, reaction times, water temperature) and write one “decision question” showing why variability matters; they must answer using centre and spread from the plots.
• Mixed ability grouping: assign roles (Data enterer, Calculator, Checker, Explainer). Rotate roles so quieter students still contribute through explanation prompts or checking.

Dyslexia-friendly options

• Provide printed data with high-contrast colours and generous spacing.
• Offer both teacher-read and student-read instructions; allow audio reading for the data set.
• Use short, step-by-step written directions on the worksheet (Step 1: enter stems; Step 2: add leaves; Step 3: count; Step 4: calculate).

Success criteria (re-stated for students)

• I can describe variability as how spread out values are.
• I can create an ordered stem-and-leaf plot.
• I can calculate range, median, mean and mode.
• I can explain how outliers and skew affect averages and conclusions.