Lesson

Interpreting distributions

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-DAT-U01-L1135–45 min

You will learn

  • Describe the centre.
  • Describe the spread.
  • Spot an outlier.
  • Choose mean or median.

Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.

Student lesson

Words to know

distribution
How data are spread.
outlier
Very different value.
skewed
Stretched on one side.
centre
Typical value.

1. Discover: one big value

Five pupils read 2, 3, 3, 4 and 18 books. Is the mean a fair “typical” value?

2. Understand: interpreting distributions

  • Mean = 30 ÷ 5 = 6; median = 3.
  • 18 is an outlier; it pulls the mean up.
  • The median describes the typical pupil better here.
  • Describe: centre, spread (range 16), shape, and any outlier.
Remember: Outliers pull the mean; the median resists.

3. Explore: describe

You need paper.

  1. Find mean and median.
  2. Find the range.
  3. Spot outliers.
  4. Write a sentence.
Think about it: what did you notice?

Median 3.

4. Practise

Guided practice

Question 1. Mean?

6.

Question 2. Median?

3.

Question 3. Outlier?

18.

Independent practice

  1. Mean of 2, 3, 3, 4, 18
  2. Median of 2, 3, 3, 4, 18
  3. Range
  4. Outlier
  5. Better typical value here

Answers are in the answer key below. Try first, then check.

5. Apply: everyday mathematics

Books read: 2,3,3,4,18. Which typical value is fairer?

Show a sample answer

The median, 3.

6. Common mistake

Mistake: Ignoring an outlier.
Fix: Name and explain it.

7. Check and master

Answer all questions. You will see feedback after each one.

1. Mean of 2, 3, 3, 4, 18:

2. Median of 2, 3, 3, 4, 18:

3. Range:

4. Outlier:

5. Better typical value:

Challenge. An outlier usually pulls the:

Your result appears here after you answer every question.

8. Key takeaways

  • Centre, spread, shape.
  • Outliers affect the mean.
  • Median resists outliers.

9. Next lesson

Next lesson: Understanding mathematical problems. Keep going with the next idea in this course.

Printable worksheet

  1. Mean of 2,3,3,4,18
  2. Median
  3. Range
  4. Outlier
  5. Better typical value

Homework

Collect data with one unusual value and describe it.

Answer key and marking scheme

Question Expected response Marks
Mean of 2,3,3,4,18 6 2
Median 3 2
Range 16 2
Outlier 18 2
Better typical value median 2
Total 10

Practice answers: Worksheet: 1 6; 2 3; 3 16; 4 18; 5 median.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Describe the centre Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Describe the spread Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Spot an outlier Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Choose mean or median Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Ignoring an outlier. Name and explain it.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Mean and median.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: describe the centre; describe the spread; spot an outlier; choose mean or median.

Prerequisite knowledge. Lessons 7–10.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 35–45 minutes.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Ignoring an outlier. Name and explain it.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Mean and median. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.

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