You will learn
- Compare two datasets.
- Say which has the greater mean.
- Compare spreads using range.
- Write a comparison.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- A dataset is a group of data.
- Compare means to compare averages.
- Compare ranges to compare spread.
- Write a short comparison using numbers.
Words to know
A group of data.
How far apart values are.
Total ÷ count.
Greatest minus least.
1. Discover: two classes
Class A scores: 5, 7, 8, 9, 11. Class B: 4, 6, 8, 10, 12. Which class did better?
2. Understand: comparing datasets
- Mean A: 40 ÷ 5 = 8. Mean B: 40 ÷ 5 = 8. Same mean.
- Median: both 8.
- Range A: 11 − 5 = 6. Range B: 12 − 4 = 8.
- Conclusion: same average, but B is more spread out.
Idea 1: Dataset A
A: 5, 7, 8, 9, 11. Total 40, mean 40 ÷ 5 = 8. Range 11 − 5 = 6. Median 8.
Idea 2: Dataset B
B: 4, 6, 8, 10, 12. Total 40, mean 8. Range 12 − 4 = 8.
Idea 3: Compare
A and B have the same mean (8), but B has the greater range, so B is more spread out.
Why both? The mean says typical; the range says spread.
3. Worked examples
Example 1 (I show you): Range
A: 5, 7, 8, 9, 11
- 11 − 5.
Answer: 6
Example 2 (We do it together): Mean
B: 4, 6, 8, 10, 12
- 40 ÷ 5.
Answer: 8
Example 3 (You try): Compare
Greater range
Show the steps and answer
- 8 vs 6.
Answer: B
Did you know?
Two datasets can have the same mean but very different spread.
Why this matters
Comparing data helps us decide which group, team or product does better.
4. Explore: compare
You need paper.
- Find each mean.
- Find each median.
- Find each range.
- Write a sentence.
Think about it: what did you notice?
Same mean, B more spread.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The mean of A is ___ and of B is ___.
- The range of A is ___ and of B is ___.
- ___ is more spread out.
- So the means are ___.
Guided practice
Question 1. Mean of A?
8.
Question 2. Range of B?
8.
Question 3. Which is more spread?
B.
Independent practice
Level 1: Start
- Range of A
- Mean of B
- Median of A
- Who has the greater range?
- Do they have the same mean?
Level 2: Grow
- Mean of 2, 4, 6
- Range of 3 and 9
- More spread: (1, 5, 9) or (4, 5, 6)?
Level 3: Stretch
- Mean of 2, 7, 12
- Range of 2, 7, 12
- Ben says a range of 6 means A has the higher mean. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A has range 6 and B has range 8. Which is more spread out?
Show a sample answer
B.
Another one. Ana scores 5, 7, 8, 9, 11 and Ben scores 4, 6, 8, 10, 12. Compare them.
Show a sample answer
Both have a mean of 8, but Ben is more spread out (range 8 vs 6).
7. Common mistakes
Fix: Compare mean and range.
Fix: Use the mean for the average.
Fix: Use both mean and range.
8. Lesson summary and revision card
- I can compare two datasets.
- I can say which has the greater mean.
- I can compare spread using range.
- I can write a comparison.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Centre and spread.
- Use a full sentence.
- Same mean can hide differences.
11. Next lesson
Next lesson: Drawing conclusions. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Find the range of A: 5, 7, 8, 9, 11. [2 marks]
- Find the mean of B: 4, 6, 8, 10, 12. [3 marks]
- Find the median of A: 5, 7, 8, 9, 11. [2 marks]
- Which of A and B has the greater range? [2 marks]
- Ali says A and B have different means because their values differ. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 11 − 5 [1]; 6 [1]
- Total 40 [1]; ÷ 5 [1]; 8 [1]
- Middle value of an ordered list [1]; 8 [1]
- A has 6 and B has 8 [1]; B [1]
- No [1]. Both totals are 40 with 5 values [1]. Both means are 8 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Range of A
- Mean of B
- Median of A
- Greater range
- Same mean? (yes/no)
- Mean of A (5, 7, 8, 9, 11):
- Mean of B (4, 6, 8, 10, 12):
- Range of A:
- Range of B:
- More spread out:
Homework
Compare the heights of two groups of five people.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Range of A | 6 | 2 |
| Mean of B | 8 | 2 |
| Median of A | 8 | 2 |
| Greater range | B | 2 |
| Same mean? (yes/no) | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 6; 2 8; 3 8; 4 B; 5 yes.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 8; 7 8; 8 6; 9 8; 10 B.
Independent practice answers. Level 1: 1 6; 2 8; 3 8; 4 B; 5 yes (both means are 8). Level 2: 1 4; 2 6; 3 (1, 5, 9). Level 3: 1 7; 2 10; 3 Range shows spread, not the average..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare two datasets | 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 Say which has the greater mean | 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 Compare spreads using range | 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 Write a comparison | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Comparing only one value. Compare mean and range.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Mean of small sets.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child compares two datasets using mean and range. You do not need to be good at mathematics to help.
- Compare two sports teams’ scores.
- Ask: which average? which spread?
- Write a sentence with numbers.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: compare two datasets; say which has the greater mean; compare spreads using range; write a comparison.
Prerequisite knowledge. Lesson 6.
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. 45–60 minutes. It can be split into two shorter sessions.
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.
Key questions. Which mean is greater? Which range is greater?
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. Comparing only one value. Compare mean and range.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Mean of small sets. 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 5 » Measurement & Data. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.SP.A.3 and 6.SP.B.5; Cambridge Primary Mathematics Stage 6 (comparing data). These sources informed the lesson.