Averages in Data

Overview

Students calculate mean, median, and mode from discrete and continuous numerical data sets and use these measures to describe “typical” values. This lesson continues from earlier work on data, range, and organising data.

Learning intentions

• WALT calculate the mean, median, and mode for a given data set.
• WALT explain which measure of centre best represents the data in context.
• WALT recognise how outliers can change mean compared with median and mode.

Success criteria

• I can compute the mean for a data set correctly.
• I can find the median using ordered data.
• I can identify the mode (and explain if there is no single mode).
• I can justify which measure of centre fits the question, using ideas about outliers and spread.

Curriculum links

• Mathematics — AC9M7ST01: acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data.
• Mathematics — AC9M7ST02: create and describe numerical data displays; compare distribution features and determine range, median, mean and mode (including commenting on outliers).
• Mathematics — AC9M7ST03: analyse and interpret distributions; report findings using shape and summary statistics.

Lesson structure (60 minutes)

1. 0–5 min · Warm-up (Conversation starters). Teacher shows three quick data snippets on the board (e.g., 6, 6, 7, 8, 20; 10, 12, 12, 13, 14; 4, 5, 5, 5, 6) and asks: “Which number would you call typical and why?” Students do a quick think, then pair-share.

2. 5–15 min · Direct teach: Mean, median, mode (Dyslexia-friendly). Teacher models each method using one clean example set, speaking through steps and writing large, numbered procedures. Students copy only the steps they will use.

• Mean: “Add all values, then divide by how many values.”
• Median: “Order the data, then pick the middle value (or average the two middle values).”
• Mode: “Find the value that occurs most often.” Teacher emphasises: “Mode and median can be more stable when there’s an outlier; mean can shift.”

3. 15–35 min · Guided practice: Step-by-step calculations. Teacher provides a worksheet with 4 short tasks. Students work in ability pairs; teacher circulates and checks method.

• Task A: Find mean for a set of 7 whole numbers.
• Task B: Find median for a set of 10 numbers (including a tie around the middle).
• Task C: Find mode for a set with two repeating values.
• Task D: “Typical value” justification: Given two data sets with the same median, ask which measure of centre best answers a context question (e.g., reaction times vs cost). Success criterion check is embedded: students must show at least one correct working step (not just the answer).

4. 35–50 min · Data choice discussion (Centre that fits). Teacher displays two ordered data sets with an outlier. Students answer on mini whiteboards:

• “Which is larger: mean of Set 1 or Set 2?”
• “For the question ‘What is a typical height?’, choose mean/median/mode and justify in one sentence.” Teacher runs a whole-class discussion, drawing out how outliers affect mean more than median, and how mode helps when values repeat.

5. 50–58 min · Independent checkpoint (Differentiated). Students complete an individual set of 3 problems (teacher pre-sorts by support level):

• Core: compute mean and median from given ordered/unsorted data (teacher gives an example of ordering).
• Support: compute median only (teacher provides partially ordered data).
• Extension: compute mean and median, then write a justification about which measure is best and whether an outlier exists. Teacher uses a quick “show your steps” rule: no steps = no mark.

6. 58–60 min · Exit ticket (1 minute answers). Exit ticket: “Data: 3, 3, 4, 7, 20. Calculate the mean and median. Which is better for ‘typical’ and why (one reason)?” Students submit.

Resources

• Large-print student worksheet (three calculation methods on the same page)
• Mini whiteboards and markers
• Number cards or a small “data sorting” mat (to order numbers for median)
• Teacher example data slides/board with steps labelled 1–4
• Coloured pens/pencils for highlighting: mean steps, median ordering, mode frequency
• Digital timer (for pacing) and a printed answer-check strip (teacher-controlled)
• Optional: pre-made number line and a “middle value” guide for median

Assessment

• Formative: teacher observation during guided practice (check for correct order for median and correct division for mean).
• Formative: mini whiteboard responses during the outlier discussion.
• Summative (informal): exit ticket accuracy and justification quality.

Differentiation

• Step-by-step instruction for all: provide a “Work method” strip for mean, median, mode on every page.
• Support group: partially ordered data for median; fewer calculations; sentence frames for justifications (“Median is better because…”).
• Extension group: include a case with no clear mode and a justification about how to describe “typical” using median/mean instead.
• Dyslexia-friendly reading options:
• Large print worksheet with ample spacing and short line lengths
• Audio read-aloud of task directions and success criteria
• Colour-coded steps (mean/median/mode)
• Sentence starters for working: “First I order… Then I find the middle…”
• EAL support: glossary at the top of the worksheet (mean, median, mode) with brief examples; encourage students to explain using numbers plus one spoken sentence before writing.