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
---
Question 1: What is the median?
Median = middle value when numbers are ordered.
Since there are 11 scores (odd number), the middle one is the
6th score.
Counting:
1st: 100
2nd: 96
3rd: 90
4th: 90
5th: 84
6th: 80 ← median
7th: 75
... etc.
✔ Median =
80
---
Question 2: What is the mode?
Mode = the number that appears most often.
Look at History scores:
- 75 appears
three times → more than any other
- 90 appears twice
- Others appear once
✔ Mode =
75
---
Question 3: What is the range?
Range = highest mark – lowest mark
Highest = 100
Lowest = 49
Range = 100 - 49 =
51
✔ Range =
51
---
Question 4: What is the mean?
Mean = add all marks together, then divide by number of marks (11)
Add them:
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 calculate:
11 × 79 = 869 → because 11×70=770, 11×9=99 → 770+99=869
✔ Mean =
79
---
Now for the
Maths test marks:
Given list:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
→ Also
11 scores, but NOT in order? Let’s check — actually, they’re listed from high to low already? Wait:
Wait — let’s sort them properly to be safe (though they look mostly sorted):
Original:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54 → yes, descending order.
But for median, we need ascending or descending — as long as ordered, middle is same.
We’ll use descending as given.
Total = 11 → median is 6th score.
Count:
1st: 100
2nd: 100
3rd: 97
4th: 85
5th: 85
6th: 82 ← median
7th: 74
8th: 74
9th: 74
10th: 66
11th: 54
✔ Question 5: Median =
82
---
Question 6: Mode of maths marks?
Which number appears most?
- 100 → twice
- 85 → twice
- 74 →
three times ← most frequent
Others: 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:
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
Sum = 891
Number of marks = 11
Mean = 891 ÷ 11
Calculate:
11 × 81 = 891 → because 11×80=880, 11×1=11 → 880+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 worksheet on mean median and mode.
