Question
A student has a mean score of 82 on 4 science quizzes. The student took a 5th quiz and scored 92. What is the student's mean score for all 5 science quizzes?
Answers
GPT-4o mini
To find the mean score for all 5 science quizzes, we first need to determine the total score for the first 4 quizzes. Since the mean score is 82 for those 4 quizzes, we can calculate the total score as follows:
\[
\text{Total score for 4 quizzes} = \text{Mean score} \times \text{Number of quizzes} = 82 \times 4 = 328
\]
Next, we add the score from the 5th quiz:
\[
\text{Total score for 5 quizzes} = \text{Total score for 4 quizzes} + \text{Score on 5th quiz} = 328 + 92 = 420
\]
Now, we calculate the mean score for all 5 quizzes:
\[
\text{Mean score for 5 quizzes} = \frac{\text{Total score for 5 quizzes}}{\text{Number of quizzes}} = \frac{420}{5} = 84
\]
Therefore, the student's mean score for all 5 science quizzes is \(\boxed{84}\).
\[
\text{Total score for 4 quizzes} = \text{Mean score} \times \text{Number of quizzes} = 82 \times 4 = 328
\]
Next, we add the score from the 5th quiz:
\[
\text{Total score for 5 quizzes} = \text{Total score for 4 quizzes} + \text{Score on 5th quiz} = 328 + 92 = 420
\]
Now, we calculate the mean score for all 5 quizzes:
\[
\text{Mean score for 5 quizzes} = \frac{\text{Total score for 5 quizzes}}{\text{Number of quizzes}} = \frac{420}{5} = 84
\]
Therefore, the student's mean score for all 5 science quizzes is \(\boxed{84}\).