Median , mode, range and mean - Statistics (Handling Data) Maths ... - Free Printable

Let's solve the problem step by step using the data provided in the worksheet.

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Part 1: History Test Marks

Scores:
100, 96, 90, 90, 84, 80, 75, 75, 75, 55, 49

There are 11 marks (odd number), so we can find the median easily.

#### 1. What is the median?
- The median is the middle value when the numbers are arranged in order.
- The list is already in descending order:
100, 96, 90, 90, 84, 80, 75, 75, 75, 55, 49
- Since there are 11 values, the median is the 6th value.
- Counting:
1. 100
2. 96
3. 90
4. 90
5. 84
6. 80 ← Median
7. 75
8. 75
9. 75
10. 55
11. 49

✔ Median = 80

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#### 2. What is the mode?
- The mode is the number that appears most frequently.
- Let's count frequencies:
- 100 → 1
- 96 → 1
- 90 → 2
- 84 → 1
- 80 → 1
- 75 → 3
- 55 → 1
- 49 → 1

✔ Mode = 75 (appears 3 times)

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#### 3. What is the range?
- Range = Highest mark − Lowest mark
- Highest = 100
- Lowest = 49
- Range = 100 − 49 = 51

✔ Range = 51

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#### 4. What is the mean?
- Mean = (Sum of all marks) ÷ (Number of marks)
- Sum = 100 + 96 + 90 + 90 + 84 + 80 + 75 + 75 + 75 + 55 + 49
Let’s add them:

Break it down:
- 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 = 79

✔ Mean = 79

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Part 2: Maths Test Marks

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

Again, 11 marks.

#### 5. What is the median?
- Arrange in order (already sorted):
100, 100, 97, 85, 85, 82, 74, 74, 74, 66, 54
- Middle value is the 6th one:
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

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#### 6. What is the mode?
- Count frequencies:
- 100 → 2
- 97 → 1
- 85 → 2
- 82 → 1
- 74 → 3
- 66 → 1
- 54 → 1

Most frequent: 74 (3 times)

✔ Mode = 74

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#### 7. What is the range?
- Highest = 100
- Lowest = 54
- Range = 100 − 54 = 46

✔ Range = 46

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#### 8. What is the mean?
- Sum = 100 + 100 + 97 + 85 + 85 + 82 + 74 + 74 + 74 + 66 + 54
Let’s calculate:

Group them:
- 100 + 100 = 200
- 97
- 85 + 85 = 170
- 82
- 74 × 3 = 222
- 66
- 54

Now add:
- 200 + 97 = 297
- 297 + 170 = 467
- 467 + 82 = 549
- 549 + 222 = 771
- 771 + 66 = 837
- 837 + 54 = 891

Total sum = 891
Number of marks = 11
Mean = 891 ÷ 11 = 81

✔ Mean = 81

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✔ Final Answers:

History Test:
1. Median = 80
2. Mode = 75
3. Range = 51
4. Mean = 79

Maths Test:
5. Median = 82
6. Mode = 74
7. Range = 46
8. Mean = 81

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