Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+60 XP
What you need:
IWB/Projector/Large Screen

Comparing Data Sets and Drawing Inferences

Compare two data sets by their centre and spread to draw inferences. Discover how two groups can share the same mean yet tell very different stories about consistency and range.

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    1 - Getting Started ~4 mins

    Illustration for Getting Started

    Key question

    Two 6th classes sat the same spelling test out of 25. Both classes had a mean score of 15. So did the two classes really do the same? Or could a single number be hiding a very different story?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~8 mins

    Here are the two classes' spelling test scores.

    • Class A: 14, 14, 15, 15, 16, 16
    • Class B: 8, 12, 15, 15, 20, 20

    Both sets have a mean of 15. Look at how far apart the lowest and highest scores are in each set. That gap is the range (the distance from the lowest to the highest score).

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Compare Sets Side by Side ~9 mins

    Now we compare three fresh pairs of data sets, not the two classes. Each pair is shown as two plots so we can read both at once:

    • Pair 1: 14, 15, 16 against 5, 15, 25
    • Pair 2: 15, 16, 17 against 9, 12, 21
    • Pair 3: 9, 10, 10, 11 against 9, 10, 10, 11, 24

    For each comparison, read off the mean and the range of both plots, then say which set is more consistent and which is more spread out.

    +10 XP

    4 - Record and Infer in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, record the mean of the Class A and Class B scores from Watch and Notice. Note which set is more spread out. Then write one inference sentence backed by a number, for example: Class A is more consistent because its range is only …, while Class B's range is ….

    +10 XP

    5 - Class Challenge ~8 mins

    We run a real class survey and compare two groups from it. Choose a question the class can answer quickly, such as how many minutes each of us spent on homework last night, or the height of two teams. We split the answers into two groups, enter each group, and read the mean and range. Then we make a claim about the two groups and back it up with at least two numbers.

    Think and discuss

    Could the group with the lower mean still be called the better one? A hook: a group whose scores are all close to typical can be more reliable even if its mean is lower.

    Compare two survey groups

    +15 XP
    Pupil practice
    Module 9 · Data and Chance Data & Chance
    Lesson 107 · Comparing Data Sets and Drawing Inferences
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