Math worksheet on median, mode, range, and mean with example problems and answer spaces.

Let’s solve each question step by step.

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History Test Scores (already in order from highest to lowest):
100, 96, 90, 90, 84, 80, 75, 75, 75, 55, 49
→ Total = 11 scores

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Question 1: Median of History test

Median is the middle number when all numbers are in order.

Since there are 11 scores (odd number), the median is the 6th score.

Counting:

1st: 100
2nd: 96
3rd: 90
4th: 90
5th: 84
6th: 80 ← median
7th: 75
8th: 75
9th: 75
10th: 55
11th: 49

✔ Median = 80

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Question 2: Mode of History test

Mode is the number that appears most often.

Look at frequencies:

- 100 → 1 time
- 96 → 1
- 90 → 2 times
- 84 → 1
- 80 → 1
- 75 → 3 times ← most frequent
- 55 → 1
- 49 → 1

✔ Mode = 75

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Question 3: Range of History test

Range = Highest – Lowest

Highest = 100
Lowest = 49
Range = 100 – 49 = 51

✔ Range = 51

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Question 4: Mean of History test

Mean = sum of all scores ÷ number of scores

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 divide:

11 × 79 = 869 → because 11×70=770, 11×9=99 → 770+99=869

✔ Mean = 79

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Now for the Maths test marks:

Scores given:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
→ Also 11 scores. But they’re NOT in order yet! We need to sort them first for median and mode.

Sort from highest to lowest (or lowest to highest — doesn’t matter as long as ordered):

Sorted:
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
Wait — actually, let’s write them in ascending order to be safe:

54, 66, 74, 74, 74, 82, 85, 85, 97, 100, 100

Yes, that’s correct.

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Question 5: Median of Maths marks

Again, 11 scores → median is the 6th one.

Counting in sorted order (ascending):

1st: 54
2nd: 66
3rd: 74
4th: 74
5th: 74
6th: 82 ← median
7th: 85
8th: 85
9th: 97
10th: 100
11th: 100

✔ Median = 82

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Question 6: Mode of Maths marks

Which number appears most?

- 54 → 1
- 66 → 1
- 74 → 3 times
- 82 → 1
- 85 → 2
- 97 → 1
- 100 → 2

So 74 appears 3 times — more than any other.

✔ Mode = 74

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Question 7: Range of Maths marks

Highest = 100
Lowest = 54
Range = 100 – 54 = 46

✔ Range = 46

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Question 8: Mean of Maths marks

Sum 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

Check: 11 × 81 = 891 → because 11×80=880, plus 11=891

✔ Mean = 81

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Final Answer:
1. 80
2. 75
3. 51
4. 79
5. 82
6. 74
7. 46
8. 81