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Math  /  Data & Statistics

QuestionThe scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 87 , the student scored 98. What is the student's new weighted mean? \begin{tabular}{lccc} & Score & \begin{tabular}{c} Percent of \\ Final Grade \end{tabular} & \begin{tabular}{c} Weighted \\ Score \end{tabular} \\ Homework & 87 & 10 & 8.7 \\ Quiz & 78 & 25 & 19.5 \\ Project & 97 & 20 & 19.4 \\ Speech & 90 & 15 & 13.5 \\ Final Exam & 87 & 30 & 26.1 \\ & & Weighted Mean & 87.2 \end{tabular}
The student's new weighted mean score is □\square (Do not round.)

Studdy Solution

STEP 1

1. The scores and their corresponding weights are given in percentages.
2. The weighted mean is calculated by multiplying each score by its weight, summing these products, and then dividing by the total weight.
3. An error occurred in the Final Exam score, which needs to be corrected from 87 to 98.
4. All weights are expressed as percentages and sum to 100%.

STEP 2

1. Calculate the original weighted mean to understand the initial state.
2. Calculate the new weighted score for the Final Exam with the corrected score.
3. Compute the total weighted score with the corrected Final Exam score.
4. Calculate the new weighted mean.

STEP 3

Calculate the original weighted mean to confirm the given value.
Weighted Mean=∑(Score×Percent of Final Grade)∑(Percent of Final Grade) \text{Weighted Mean} = \frac{\sum (\text{Score} \times \text{Percent of Final Grade})}{\sum (\text{Percent of Final Grade})}
Given data: \begin{align*} \text{Homework} & : 87 \times 0.10 = 8.7 \\ \text{Quiz} & : 78 \times 0.25 = 19.5 \\ \text{Project} & : 97 \times 0.20 = 19.4 \\ \text{Speech} & : 90 \times 0.15 = 13.5 \\ \text{Final Exam} & : 87 \times 0.30 = 26.1 \\ \end{align*}
Summing these weighted scores gives: 8.7+19.5+19.4+13.5+26.1=87.2 8.7 + 19.5 + 19.4 + 13.5 + 26.1 = 87.2

STEP 4

Calculate the new weighted score for the Final Exam with the corrected score of 98.
New Weighted Score for Final Exam=98×0.30=29.4 \text{New Weighted Score for Final Exam} = 98 \times 0.30 = 29.4

STEP 5

Compute the total weighted score with the corrected Final Exam score.
Original total weighted score without Final Exam: 8.7+19.5+19.4+13.5=61.1 8.7 + 19.5 + 19.4 + 13.5 = 61.1
Add the corrected Final Exam weighted score: 61.1+29.4=90.5 61.1 + 29.4 = 90.5

STEP 6

Calculate the new weighted mean.
New Weighted Mean=90.51.00=90.5 \text{New Weighted Mean} = \frac{90.5}{1.00} = 90.5
The student's new weighted mean score is 90.590.5.

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