Basic Math and Pre-Algebra - Probabilities and Statistics

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5. Study Guide Answer Choices • The mean is larger than the median. • The mode is larger than the mean. • The median, the mean, and the mode all have the same value. Correct Answer ࿨ ࿩ ࿪ The median, the mean, and the mode all have the same value. Why This Is Correct For the numbers 17, 10, 16, 17: Ordered: 10, 16, 17, 17 Median = (16 + 17) ÷ 2 = 16.5 Mode = 17 Mean = 15 Actually, none of the choices are true based on calculation. However, based on typical textbook intention, the closest correct choice would need clarification. 9. Question If the mean of 8 scores is 12, then which of the following MUST be true? Answer Choices • All the scores added together must be more than 90. • At least 3 scores are less than 12. • Both A and B must be true. Correct Answer ࿨ ࿩ ࿪ All the scores added together must be more than 90.

6. Study Guide Why This Is Correct Mean = 12 Total = 12 × 8 = 96 96 is more than 90. 10. Question If all tests have equal value, then what would be the mean of 4 tests averaging 60% plus 6 tests averaging 70%? Answer Choices • less than 65% • 65% • more than 65% Correct Answer ࿨ ࿩ ࿪ 66% (more than 65%) Why This Is Correct (4 × 60) + (6 × 70) = 240 + 420 = 660 660 ÷ 10 = 66% 66% is more than 65%. 11. Question If 4 people each weigh 85 pounds and 8 people each weigh 90 pounds, then what is the average weight for all 12 people? Answer Choices • 87(1/2) pounds • 88(1/3) pounds • 88.4 pounds

7. Study Guide Correct Answer ࿨ ࿩ ࿪ 88(1/3) pounds Why This Is Correct (4 × 85) + (8 × 90) = 340 + 720 = 1060 1060 ÷ 12 = 88.33… = 88(1/3) 12. Question What is the median for the monthly rainfall totals? Answer Choices • 12 • 14 • 15 Correct Answer ࿨ ࿩ ࿪ Cannot be determined Why This Is Correct The rainfall data is not provided, so the median cannot be calculated. 13. Question A student has a mean of 70% on her first 4 tests. What must she get on the fifth test so that her mean will now be 75%? Answer Choices • 80% • 90% • 95%

8. Study Guide Correct Answer ࿨ ࿩ ࿪ 95% Why This Is Correct First 4 tests total: 4 × 70 = 280 To average 75 over 5 tests: 5 × 75 = 375 375 − 280 = 95 She must score 95%. 14. Question Set A: 12, 15, 37, 10, 11 Set B: 3, 58, 17, 7 Answer Choices • The median of set A equals the median of set B. • The mean of set A equals the mean of set B. • Both A and B are true. Correct Answer ࿨ ࿩ ࿪ The mean of set A equals the mean of set B. Why This Is Correct Set A mean: (12 + 15 + 37 + 10 + 11) ÷ 5 = 85 ÷ 5 = 17 Set B mean: (3 + 58 + 17 + 7) ÷ 4 = 85 ÷ 4 = 21.25 Actually, the means are not equal. Set A median = 12 Set B median = 12 Correct Answer: ࿨ ࿩ ࿪ The median of set A equals the median of set B.

9. Study Guide 15. Question Set Q: 4, 10, 12, 7, 19, 10, 5, w Answer Choices • 13 • 17 • 21 Correct Answer ࿨ ࿩ ࿪ 13 Why This Is Correct When w = 13: Ordered set: 4, 5, 7, 10, 10, 12, 13, 19 Median = (10 + 10) ÷ 2 = 10 Mode = 10 Mean = (80 + 13) ÷ 8 = 93 ÷ 8 = 11.625 Actually, none of the given answers make mean, median, and mode equal based on calculation. The question may require review. 2. Probability Probability tells us how likely something is to happen. It is a number that measures the chance of an event occurring. When all outcomes are equally likely, we use this formula: In simple words: Count the outcomes you want. Divide by all possible outcomes.

10. Study Guide Example 1: One Spinner Suppose a spinner has 10 equal sections labeled 1 through 10. What is the probability of spinning a 6? There is: • 1 favorable outcome (landing on 6) • 10 total possible outcomes ࿨ ࿩ ࿪ The probability is 1/10 . Figure 1 Example 2: Two Possible Results What is the probability of spinning either a 3 or a 5?