Let’s solve each question step by step.
---
First, look at the History test scores:
They are listed in order from highest to lowest:
100, 96, 90, 90, 84,
80, 75, 75, 75, 55, 49
There are
11 scores.
---
Question 1: What is the median?
The
median is the middle number when all numbers are in order.
Since there are 11 numbers (odd), the middle one is the
6th number.
Count them:
1st: 100
2nd: 96
3rd: 90
4th: 90
5th: 84
6th: 80 ← this is the median
✔ Median =
80
---
Question 2: What is the mode?
The
mode is the number that appears most often.
Look at the list:
- 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?
The
range is the difference between the highest and lowest mark.
Highest = 100
Lowest = 49
Range = 100 - 49 =
51
✔ Range =
51
---
Question 4: What is the mean?
The
mean is the average. Add all marks together, then divide by how many there are (11).
Add them:
Start adding step by step:
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 marks =
11
Mean = 869 ÷ 11
Let’s divide:
11 × 79 = 869 → because 11×70=770, 11×9=99 → 770+99=869
✔ Mean =
79
---
Now, move to the
Maths test marks:
List:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
Again, 11 marks — already in order? Let’s check:
From high to low: yes, it looks sorted.
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
---
Question 5: Median of maths marks?
Middle number = 6th number (since 11 total)
Count:
1st: 100
2nd: 100
3rd: 97
4th: 85
5th: 85
6th: 82 ← median
✔ Median =
82
---
Question 6: Mode of maths marks?
Which number appears most?
- 100 → twice
- 97 → once
- 85 → twice
- 82 → once
- 74 →
three times ← most!
- 66 → once
- 54 → once
✔ Mode =
74
---
Question 7: Range of maths marks?
Highest = 100
Lowest = 54
Range = 100 - 54 =
46
✔ Range =
46
---
Question 8: Mean of maths marks?
Add all marks:
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 marks =
11
Mean = 891 ÷ 11
Let’s 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 mode median range worksheet.
