This worksheet guides students through finding the median, mode, range, and mean using sets of test scores.

Problem Analysis:

The task involves calculating the median, mode, range, and mean for two sets of test scores. Let's solve each part step by step.

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Part 1: History Test Scores

The given scores are:
\[ 100, \, 96, \, 90, \, 90, \, 84, \, 80, \, 75, \, 75, \, 75, \, 55, \, 49 \]

#### 1. Median
- The median is the middle value when the data is arranged in ascending order.
- Since there are 11 scores (an odd number), the median is the 6th value in the ordered list.
- The scores are already in ascending order.
- The 6th value is 80.

Median = 80

#### 2. Mode
- The mode is the value that appears most frequently.
- From the list, the number 75 appears three times, which is more frequent than any other number.
- Therefore, the mode is 75.

Mode = 75

#### 3. Range
- The range is the difference between the highest and lowest values.
- Highest score = 100
- Lowest score = 49
- Range = \( 100 - 49 = 51 \)

Range = 51

#### 4. Mean
- The mean is calculated by summing all the scores and dividing by the total number of scores.
- Sum of scores:
\[
100 + 96 + 90 + 90 + 84 + 80 + 75 + 75 + 75 + 55 + 49 = 869
\]
- Total number of scores = 11
- Mean = \( \frac{869}{11} = 79 \)

Mean = 79

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Part 2: Maths Test Scores

The given scores are:
\[ 100, \, 100, \, 97, \, 85, \, 85, \, 82, \, 74, \, 74, \, 74, \, 66, \, 54 \]

#### 5. Median
- The median is the middle value when the data is arranged in ascending order.
- Since there are 11 scores (an odd number), the median is the 6th value in the ordered list.
- The scores are already in ascending order.
- The 6th value is 82.

Median = 82

#### 6. Mode
- The mode is the value that appears most frequently.
- From the list, the number 74 appears three times, which is more frequent than any other number.
- Therefore, the mode is 74.

Mode = 74

#### 7. Range
- The range is the difference between the highest and lowest values.
- Highest score = 100
- Lowest score = 54
- Range = \( 100 - 54 = 46 \)

Range = 46

#### 8. Mean
- The mean is calculated by summing all the scores and dividing by the total number of scores.
- Sum of scores:
\[
100 + 100 + 97 + 85 + 85 + 82 + 74 + 74 + 74 + 66 + 54 = 891
\]
- Total number of scores = 11
- Mean = \( \frac{891}{11} = 81 \)

Mean = 81

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Final Answers:

1. Median (History) = 80
2. Mode (History) = 75
3. Range (History) = 51
4. Mean (History) = 79
5. Median (Maths) = 82
6. Mode (Maths) = 74
7. Range (Maths) = 46
8. Mean (Maths) = 81

\boxed{80, 75, 51, 79, 82, 74, 46, 81}