Question
Ally has taken 5 quizzes this year. Her mean quiz score is 8 out of 10. She takes another quiz and gets a perfect score of 10. What happens to her mean score? The mean increases by 2. The mean increases by 0.33. The mean does not change. The mean decreases by 5.
Answers
GPT-4o mini
To find out how Ally's mean score changes after taking another quiz, let's calculate her current total score and then find the new mean after adding her latest score.
1. **Calculate her current total score:**
- She has taken 5 quizzes with an average score of 8.
- Total score = Mean score × Number of quizzes = 8 × 5 = 40.
2. **Add her new quiz score:**
- She scores a perfect 10 on her next quiz.
- New total score = Previous total score + New score = 40 + 10 = 50.
3. **Calculate the new mean score:**
- Now, she has taken 6 quizzes (5 previous + 1 new).
- New mean score = New total score ÷ Number of quizzes = 50 ÷ 6 ≈ 8.33.
4. **Find the change in the mean:**
- Original mean = 8.
- New mean = 8.33.
- Change in mean = New mean - Original mean = 8.33 - 8 = 0.33.
The mean increases by 0.33.
1. **Calculate her current total score:**
- She has taken 5 quizzes with an average score of 8.
- Total score = Mean score × Number of quizzes = 8 × 5 = 40.
2. **Add her new quiz score:**
- She scores a perfect 10 on her next quiz.
- New total score = Previous total score + New score = 40 + 10 = 50.
3. **Calculate the new mean score:**
- Now, she has taken 6 quizzes (5 previous + 1 new).
- New mean score = New total score ÷ Number of quizzes = 50 ÷ 6 ≈ 8.33.
4. **Find the change in the mean:**
- Original mean = 8.
- New mean = 8.33.
- Change in mean = New mean - Original mean = 8.33 - 8 = 0.33.
The mean increases by 0.33.