Which of the scores of the three groups is more variable given their range as follows:

Variability is measured by the range. A larger range indicates greater variability.

• Group A: Range = 16
• Group B: Range = 8
• Group C: Range = 11 Comparing the ranges, 16 is the largest. 6. Which of the scores of the three groups is more variable given their range as follows? Answer: $\boxed{\text{Group A}}$

To find if an exam has a failing mark (below 75), we need to calculate the lowest score for each exam using the formula: $\text{Lowest Score} = \text{Highest Score} - \text{Range}$.

For Mathematics A:

• Highest Score = 86
• Range = 12

$$\text{Lowest Score (Math A)} = 86 - 12 = 74$$

For Mathematics B:

• Highest Score = 82
• Range = 3

$$\text{Lowest Score (Math B)} = 82 - 3 = 79$$

The passing score is 75. Mathematics A has a lowest score of 74, which is below 75. 7. If the passing score must be 75 and up, which of the two exams has an examinee with a failing mark? Answer: $\boxed{\text{Mathematics A}}$

To find the lowest score for each exam, use the formula: $\text{Lowest Score} = \text{Recorded Highest Score} - \text{Range}$.

For English:

• Highest Score = 92
• Range = 27

$$\text{Lowest Score (English)} = 92 - 27 = 65$$

For Mathematics:

• Highest Score = 88
• Range = 10

$$\text{Lowest Score (Mathematics)} = 88 - 10 = 78$$

For Science:

• Highest Score = 81
• Range = 10

$$\text{Lowest Score (Science)} = 81 - 10 = 71$$

Comparing the lowest scores (English: 65, Mathematics: 78, Science: 71), English has the lowest score. 8. Which exam recorded to have the lowest score? Answer: $\boxed{\text{English}}$

We need to find which exam has no grade lower than 75%. This means the lowest score for that exam must be 75% or higher.
From Step 3:

• Lowest Score (English) = 65
• Lowest Score (Mathematics) = 78
• Lowest Score (Science) = 71 Only Mathematics has a lowest score (78) that is 75% or higher. 9. Which exam has no grade lower than 75%? Answer: $\boxed{\text{Mathematics}}$

Variability is indicated by the range. The exam with the largest range is more variable.

• English: Range = 27
• Mathematics: Range = 10
• Science: Range = 10 Comparing the ranges, English has the largest range of 27. 10. Which set of scores is more variable? Answer: $\boxed{\text{English}}$