Distributions and Displays

Overview

This lesson is Lesson 30 of 30 in the unit “Exploring Statistics and Probability”. Students consolidate how to create and interpret numerical data displays, focusing on stem-and-leaf plots and the story they tell about distribution shape, centre, spread, outliers, and key summary measures.

Learning intentions

Students will:

• create an ordered stem-and-leaf plot from a numerical data set using appropriate software or paper
• describe and compare distributions using shape (symmetry/skew), centre (median/mean/mode), spread (range), and outliers
• determine and justify the range, median, mean and mode for a data set, including the impact of extreme values

Success criteria

Students can:

• correctly produce an ordered stem-and-leaf plot with stems and leaves in the right places
• state whether a distribution is symmetric or skewed and identify where the median sits in context
• calculate range, median, mean and mode and explain any differences due to outliers
• compare two displays by referring to shape and at least two summary statistics

Curriculum links

• Statistics and probability: create different types of numerical data displays including stem-and-leaf plots; describe and compare distribution shape, centre and spread including outliers; determine range, median, mean and mode
• Statistics: make decisions about which central tendency measure is useful for understanding the distribution
• Statistical investigations: interpret distributions and report findings in terms of shape and summary statistics

Lesson structure (60 minutes)

1. 0–5 min · Hook (conversation starter). Teacher displays two short data sets (or images of two stem-and-leaf plots) and asks: “Which looks right-skewed and how can you tell?” Students do a quick think-pair-share and justify using one sentence.

2. 5–15 min · Mini-lesson: stem-and-leaf + reading the story. Teacher models how to build an ordered stem-and-leaf plot (choose stems, split tens, list leaves in order) and then reads it: identify clusters, gaps, skewness, outliers, and locate median relative to mean. Students follow along with a partially completed example and complete one missing stem line.

3. 15–30 min · Guided practice (create a class-style display). Students work in pairs on a provided data set (continuous or discrete values, e.g., heights in cm rounded to whole numbers, or reaction times in ms as integers).

• Step A: order the data and construct the stem-and-leaf plot.
• Step B: label stems clearly and ensure leaves are in ascending order. Teacher circulates, checks plot accuracy, and uses conversation prompts: “Where do you see the biggest cluster?” “Any possible outliers?”

Success criteria check: teacher records one “done correctly” and one “common error” example for whole-class feedback.

4. 30–45 min · Calculations and interpretation (centre, spread, outliers). Students calculate range, median, mean and mode for their data and write a short distribution description. Sentence starters on the board:

• “The distribution is ___ because …”
• “The centre is best described by ___ since …”
• “The mean/median differ because …” (use outlier reasoning)

Teacher provides one worked “mean vs median with skew” example and asks: “If we removed the extreme value, what might happen to mean?”

Built-in success criteria check: students underline the outlier (if any) in the stem-and-leaf plot and connect it to the mean.

5. 45–55 min · Compare two distributions (small-group debate). Each group gets a second data set and a partially prepared stem-and-leaf plot. Students compare their own set and the new one using a simple template:

• Shape: symmetric/right-skew/left-skew
• Centre: median and mode (and mean if appropriate)
• Spread: range
• Outliers: yes/no and effect on mean/median Teacher facilitates a class discussion: “Which measure would you report to argue your conclusion, and why?”

6. 55–60 min · Exit ticket. Individually, students answer:

• “Write one similarity and one difference between the two distributions using shape and spread.”
• “State the range and the median for one display (show working or explain method).”

Resources

• Pre-prepared data sets (2) with clearly defined units and instructions
• Stem-and-leaf plot templates (paper) with labeled stems
• Data ordering strips/cards for hands-on arrangement (optional)
• Calculators (optional) and/or teacher-approved digital tool for mean calculations
• Projector/board examples of correct vs incorrect stem-and-leaf plots
• “Sentence starters” scaffold sheet
• Exit ticket slips
• Dyslexia-friendly reading materials: larger font versions and reduced-text prompts

Assessment

• Formative: teacher checks stem-and-leaf plot accuracy during circulation (correct ordering and placement of leaves)
• Formative: listen for correct justification of skewness and outliers using distribution language
• Exit ticket: compare distributions using one shape feature and one spread measure; accuracy of range/median

Differentiation

• Support: provide a step-by-step stem-and-leaf checklist (choose stems, list leaves in order, verify counts) and a “worked example” card for one median/range calculation
• Support (sentence starters): offer three levels of writing frames (basic/standard/extension) for distribution descriptions
• Extension: ask students to predict which central measure is most representative (mean vs median) and justify using skewness and outliers
• EAL/SEN: allow oral explanation recorded by the student (audio or teacher scribe) before writing; highlight key terms with icons (median = middle marker, range = start-to-end arrows)
• Dyslexia-friendly options: provide large-print data handouts, colour-consistent stems, and audio-read instructions; minimise copying by letting students use printed stem templates

Success criteria (summary for each lesson segment)

• Hook: students give one reasoned claim about skewness
• Mini-lesson: students complete one missing stem-and-leaf entry correctly
• Guided practice: students create an ordered stem-and-leaf plot with correct leaves
• Calculations: students correctly state range, median, mean, and mode and link outliers to mean/median differences
• Comparison: students use shape + spread to compare two distributions accurately in writing or speech
• Exit ticket: students accurately report range/median and one similarity/difference using data language