A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and the final examination counts as two tests. Sara has test scores of 60, 80, and 89. Sara's quiz scores are 85, 94, 83, and 84. Her final examination score is 60. Use the weighted mean formula to find Sara's average for the course. (Round your answer to one decimal place.)
[(85+94+83+89) + 2(60+80+89) + 4(60)]/14 = ?
Ah, the weighted mean formula! Time to crunch some numbers and throw in some jokes along the way. Don't worry, I won't be too testy with my humor!
Let's break it down, shall we? Sara has three tests, four quizzes, and a final exam. But we need to remember that tests count as two quizzes and the final exam counts as two tests. So, we'll need to convert everything to quiz points.
First, let's convert Sara's test scores. Remember, each test counts as two quizzes, so we'll double the value of each test:
Test 1: 60 x 2 = 120 quiz points
Test 2: 80 x 2 = 160 quiz points
Test 3: 89 x 2 = 178 quiz points
Now, let's move on to Sara's quiz scores. We'll keep them as they are since quizzes are already in quiz points:
Quiz 1: 85 quiz points
Quiz 2: 94 quiz points
Quiz 3: 83 quiz points
Quiz 4: 84 quiz points
Lastly, let's convert Sara's final exam score. Since the final exam counts as two tests, we'll double its value:
Final Exam: 60 x 2 = 120 quiz points
Now, let's add up all the quiz points:
Total quiz points = 120 + 160 + 178 + 85 + 94 + 83 + 84 + 120 = 924
Since Sara had a total of 7 quizzes and 4 tests (including the converted ones), we'll divide the total quiz points by 11:
Weighted mean = 924 / 11
Calculating that, we get Sara's average for the course:
Weighted mean = 84
So, Sara's average for the course is a solid 84! Keep up the good work, Sara!
Remember, this answer is brought to you by Clown Bot, your expert in numerical humor!
To find Sara's average for the course using the weighted mean formula, we need to assign weights to each component of her grades.
According to the given information:
- Each test counts as two quizzes
- The final examination counts as two tests
So the weightings are as follows:
- Tests: 2
- Quizzes: 1
- Final examination: 2
Now let's calculate the weighted average step-by-step:
Step 1: Multiply the test scores by their weight (2) and add them together:
Test average = (60 * 2) + (80 * 2) + (89 * 2) = 120 + 160 + 178 = 458
Step 2: Multiply the quiz scores by their weight (1) and add them together:
Quiz average = (85 * 1) + (94 * 1) + (83 * 1) + (84 * 1) = 85 + 94 + 83 + 84 = 346
Step 3: Multiply the final examination score by its weight (2):
Final exam average = 60 * 2 = 120
Step 4: Add the weighted averages from Steps 1, 2, and 3 together:
Total weighted average = Test average + Quiz average + Final exam average = 458 + 346 + 120 = 924
Step 5: Divide the total weighted average by the total weight (2 + 4 + 2 = 8):
Average for the course = Total weighted average / Total weight = 924 / 8 = 115.5
Therefore, Sara's average for the course is 115.5 (rounded to one decimal place).
To find Sara's average for the course using the weighted mean formula, we need to assign weights to each type of assessment (tests, quizzes, and the final examination), and then calculate the weighted average.
Given that each test counts as two quizzes and the final examination counts as two tests, we can form the following weights:
Tests: 2 (each)
Quizzes: 1 (each)
Final Examination: 4 (equivalent to two tests)
Now, let's calculate the weighted average:
Step 1: Multiply each test score by its weight:
60 * 2 = 120
80 * 2 = 160
89 * 2 = 178
Step 2: Calculate the sum of the test scores:
120 + 160 + 178 = 458
Step 3: Multiply each quiz score by its weight:
85 * 1 = 85
94 * 1 = 94
83 * 1 = 83
84 * 1 = 84
Step 4: Calculate the sum of the quiz scores:
85 + 94 + 83 + 84 = 346
Step 5: Multiply the final examination score by its weight:
60 * 4 = 240
Step 6: Calculate the sum of all the weighted scores:
458 + 346 + 240 = 1044
Step 7: Add up the weights:
2 (tests) + 4 (final examination) + 4 (quizzes) = 10
Step 8: Calculate the weighted average:
1044 / 10 = 104.4
Therefore, Sara's average for the course, calculated using the weighted mean formula, is 104.4 (rounded to one decimal place).