This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Step 1: Answer Question 6. 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: Group A Step 2: Answer Question 7. To find if an exam has a failing mark (below 75), we need to calculate the lowest score for each exam using the formula: Lowest Score = Highest Score - Range. For Mathematics A: Highest Score = 86 Range = 12 Lowest Score (Math A) = 86 - 12 = 74 For Mathematics B: Highest Score = 82 Range = 3 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: Mathematics A Step 3: Answer Question 8. To find the lowest score for each exam, use the formula: Lowest Score = Recorded Highest Score - Range. For English: Highest Score = 92 Range = 27 Lowest Score (English) = 92 - 27 = 65 For Mathematics: Highest Score = 88 Range = 10 Lowest Score (Mathematics) = 88 - 10 = 78 For Science: Highest Score = 81 Range = 10 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: English Step 4: Answer Question 9. 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: Mathematics Step 5: Answer Question 10. 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: English Got more? Send 'em.