Understanding Statistics

Overview

Lesson 17 of 20 in “Mastering Maths Concepts” builds students’ foundational statistics understanding by calculating and interpreting mean, median and mode for small datasets, then making fair statements about what the measures suggest.

Learning intentions

Students will:

• calculate the mean, median and mode for a set of values
• compare what each measure tells us about the centre of a distribution
• identify the effect of different data patterns (including outliers) on mean versus median
• communicate conclusions using appropriate statistical language and acknowledging uncertainty when needed

Success criteria

Students can:

• find the mean, median and mode correctly and explain how they obtained each value
• match the “best” measure of centre to a given dataset (and justify why)
• describe how changing one value (e.g., an outlier) affects mean and median differently
• use correct language such as “typical”, “most common”, “middle value”, and “average”

Curriculum links

• Mathematics — Statistics: plan and conduct statistical investigations using samples to make fair inferences, acknowledging uncertainty - Mathematics — compare variations in distributions and proportions from random samples, and recognise the effect of sample size - Mathematics — analyse and report on distributions from primary and secondary sources using random/non-random sampling ## Lesson structure (30 minutes)

1. 0–3 min · Hook. Teacher displays three short number sets on the board: A = {2, 2, 3, 10}, B = {2, 2, 3, 4}, C = {5, 5, 5, 6}. Students do a quick think: “Which set feels most ‘typical’ and why?”

2. 3–10 min · Direct teach (centre measures). Teacher models how to find:

• Mode (most frequent value)
• Median (middle value when ordered)
• Mean (sum ÷ number of values) Teacher emphasises interpretation: mean can be pulled by extreme values; median is more stable with outliers. Students compute mean/median/mode for set A together, using a worked example and ordering steps.

3. 10–17 min · Guided practice (interpretation). Teacher gives sets B and C and asks: “Which measure(s) represent the typical value best?” Students work in pairs (or individually if needed) to calculate all three measures for B and C, then write one sentence each:

• what the measure says about the data
• how you know (e.g., “middle value” or “pulled by a large value”)

4. 17–24 min · Data pattern challenge (outlier impact). Teacher introduces a micro-scenario: “A class records the time (minutes) students read at home. Last week: {12, 12, 13, 40}. This week: {12, 12, 13, 14}.” Students calculate mean and median for both weeks and answer:

• Why did the mean change more than the median?
• Which measure would you use to describe the typical reading time to the class?

5. 24–28 min · Mini investigation (sample and fairness). Teacher explains briefly: we rarely have the whole population, so we use sample data and make cautious statements. Teacher asks students to imagine taking a sample of 5 students’ favourite sports and comparing it to “everyone” in the school. Students complete a short response: “What could make our conclusion unreliable?” (Examples: small sample size, not random, missing groups.)

6. 28–30 min · Exit check. Teacher collects an exit ticket:

• Dataset D = {3, 7, 7, 9, 12}. Find mean, median, mode.
• One line: “Which measure best describes the typical value and why?”

Resources

• Board/projector with the three starter datasets and scenario numbers
• Student worksheet (or notebook page) with three columns for mean/median/mode and space for justification
• Calculator (optional) for mean checking
• Paper for ordering data (especially for median)
• Timer for steps and exit ticket

Assessment

• Teacher observation during guided practice: correct ordering for median and correct arithmetic for mean
• Listening to student justifications: whether they connect interpretation to outliers and “most common”
• Exit ticket checking: accuracy of mean/median/mode and a reasoned statement about “typical value”

Differentiation

• Support: provide a sentence frame for justification: “The typical value is best shown by ___ because ___.”
• Support: offer a worked template for mean (sum then divide), and a reminder for median (“order first, then choose the middle”).
• Extension: ask students to modify one value in a dataset and predict whether mean or median will change more, before calculating.
• EAL/SEN: allow use of additional examples, and accept verbal explanations recorded by the student in simple steps (e.g., underline the median after ordering).