Mean Mode Median Worksheets | Mean Mode Median and Range Worksheets - Free Printable
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Step-by-step solution for: Mean Mode Median Worksheets | Mean Mode Median and Range Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Mean Mode Median Worksheets | Mean Mode Median and Range Worksheets
Let’s solve each question step by step.
---
History Test Scores (already in order from highest to lowest):
100, 96, 90, 90, 84, 80, 75, 75, 75, 55, 49
→ Total of 11 scores
---
The median is the middle number when all numbers are in order.
Since there are 11 scores (odd number), the middle one is the 6th score.
Counting:
1. 100
2. 96
3. 90
4. 90
5. 84
6. 80 ← this is the median
7. 75
8. 75
9. 75
10. 55
11. 49
✔ Median = 80
---
The mode is the number that appears most often.
Look at the scores:
- 100 → once
- 96 → once
- 90 → twice
- 84 → once
- 80 → once
- 75 → three times ← most frequent
- 55 → once
- 49 → once
✔ Mode = 75
---
Range = Highest score – Lowest score
Highest = 100
Lowest = 49
Range = 100 – 49 = 51
✔ Range = 51
---
Mean = Add all scores together, then divide by how many scores there are (11).
Add them up:
100 + 96 = 196
196 + 90 = 286
286 + 90 = 376
376 + 84 = 460
460 + 80 = 540
540 + 75 = 615
615 + 75 = 690
690 + 75 = 765
765 + 55 = 820
820 + 49 = 869
Total sum = 869
Number of scores = 11
Mean = 869 ÷ 11
Let’s calculate:
11 × 79 = 869 → because 11×70=770, 11×9=99 → 770+99=869
✔ Mean = 79
---
Now for the Maths test marks:
Scores given:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
→ Also 11 scores
But note: They are NOT in order! Let’s sort them from highest to lowest (or lowest to highest — doesn’t matter as long as we’re consistent). We’ll do highest to lowest to match the History example.
Sorted Maths scores:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
Wait — actually, let’s write them clearly in descending order:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54 → already sorted? Let’s check:
Yes:
100 > 100 > 97 > 85 > 85 > 82 > 74 > 74 > 74 > 66 > 54 → correct.
Actually, wait — 85 and 85 are equal, so it’s fine. But let’s list positions:
Position 1: 100
Position 2: 100
Position 3: 97
Position 4: 85
Position 5: 85
Position 6: 82
Position 7: 74
Position 8: 74
Position 9: 74
Position 10: 66
Position 11: 54
---
Again, 11 scores → middle is the 6th score.
Count:
1. 100
2. 100
3. 97
4. 85
5. 85
6. 82 ← median
7. 74
8. 74
9. 74
10. 66
11. 54
✔ Median = 82
---
Which number appears most often?
- 100 → twice
- 97 → once
- 85 → twice
- 82 → once
- 74 → three times ← most frequent
- 66 → once
- 54 → once
✔ Mode = 74
---
Highest = 100
Lowest = 54
Range = 100 – 54 = 46
✔ Range = 46
---
Add all scores:
Start adding:
100 + 100 = 200
200 + 97 = 297
297 + 85 = 382
382 + 85 = 467
467 + 82 = 549
549 + 74 = 623
623 + 74 = 697
697 + 74 = 771
771 + 66 = 837
837 + 54 = 891
Total sum = 891
Number of scores = 11
Mean = 891 ÷ 11
Calculate:
11 × 81 = 891 → because 11×80=880, plus 11=891
✔ Mean = 81
---
Final Answer:
1. 80
2. 75
3. 51
4. 79
5. 82
6. 74
7. 46
8. 81
---
History Test Scores (already in order from highest to lowest):
100, 96, 90, 90, 84, 80, 75, 75, 75, 55, 49
→ Total of 11 scores
---
Question 1: What is the median?
The median is the middle number when all numbers are in order.
Since there are 11 scores (odd number), the middle one is the 6th score.
Counting:
1. 100
2. 96
3. 90
4. 90
5. 84
6. 80 ← this is the median
7. 75
8. 75
9. 75
10. 55
11. 49
✔ Median = 80
---
Question 2: What is the mode?
The mode is the number that appears most often.
Look at the scores:
- 100 → once
- 96 → once
- 90 → twice
- 84 → once
- 80 → once
- 75 → three times ← most frequent
- 55 → once
- 49 → once
✔ Mode = 75
---
Question 3: What is the range?
Range = Highest score – Lowest score
Highest = 100
Lowest = 49
Range = 100 – 49 = 51
✔ Range = 51
---
Question 4: What is the mean?
Mean = Add all scores together, then divide by how many scores there are (11).
Add them up:
100 + 96 = 196
196 + 90 = 286
286 + 90 = 376
376 + 84 = 460
460 + 80 = 540
540 + 75 = 615
615 + 75 = 690
690 + 75 = 765
765 + 55 = 820
820 + 49 = 869
Total sum = 869
Number of scores = 11
Mean = 869 ÷ 11
Let’s calculate:
11 × 79 = 869 → because 11×70=770, 11×9=99 → 770+99=869
✔ Mean = 79
---
Now for the Maths test marks:
Scores given:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
→ Also 11 scores
But note: They are NOT in order! Let’s sort them from highest to lowest (or lowest to highest — doesn’t matter as long as we’re consistent). We’ll do highest to lowest to match the History example.
Sorted Maths scores:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
Wait — actually, let’s write them clearly in descending order:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54 → already sorted? Let’s check:
Yes:
100 > 100 > 97 > 85 > 85 > 82 > 74 > 74 > 74 > 66 > 54 → correct.
Actually, wait — 85 and 85 are equal, so it’s fine. But let’s list positions:
Position 1: 100
Position 2: 100
Position 3: 97
Position 4: 85
Position 5: 85
Position 6: 82
Position 7: 74
Position 8: 74
Position 9: 74
Position 10: 66
Position 11: 54
---
Question 5: What is the median of the maths marks?
Again, 11 scores → middle is the 6th score.
Count:
1. 100
2. 100
3. 97
4. 85
5. 85
6. 82 ← median
7. 74
8. 74
9. 74
10. 66
11. 54
✔ Median = 82
---
Question 6: What is the mode of the maths marks?
Which number appears most often?
- 100 → twice
- 97 → once
- 85 → twice
- 82 → once
- 74 → three times ← most frequent
- 66 → once
- 54 → once
✔ Mode = 74
---
Question 7: What is the range of the maths marks?
Highest = 100
Lowest = 54
Range = 100 – 54 = 46
✔ Range = 46
---
Question 8: What is the mean of the maths marks?
Add all scores:
Start adding:
100 + 100 = 200
200 + 97 = 297
297 + 85 = 382
382 + 85 = 467
467 + 82 = 549
549 + 74 = 623
623 + 74 = 697
697 + 74 = 771
771 + 66 = 837
837 + 54 = 891
Total sum = 891
Number of scores = 11
Mean = 891 ÷ 11
Calculate:
11 × 81 = 891 → because 11×80=880, plus 11=891
✔ Mean = 81
---
Final Answer:
1. 80
2. 75
3. 51
4. 79
5. 82
6. 74
7. 46
8. 81
Parent Tip: Review the logic above to help your child master the concept of mean median and mode worksheets.
