Math Problem Statement
Solution
The problem from the image is asking to calculate the mean score of five additional students, given the mean score of a group of 30 students and the combined mean when these five students are added. Here's a breakdown of how to approach it:
Problem Setup:
- The mean score of 30 students is 7.7.
- When the scores of 5 additional students are added, the new mean becomes 8.0.
- We need to find the mean score of these 5 additional students.
Let:
- be the number of students in the first group.
- be the mean of the first group of 30 students.
- be the number of students in the second group (the additional students).
- is the unknown mean score of the second group (what we're solving for).
- The combined group has students, and the combined mean is 8.0.
Equation Setup:
We know that the total score of each group is the number of students multiplied by their respective means.
- Total score of the first group = .
- Total score of the second group = .
- Combined total score = .
Now, setting up the equation for the combined group:
Solving for :
So, the mean score of the additional 5 students is 9.8, which corresponds to option a.
Would you like further clarification or details on this solution?
Here are 5 related questions for further exploration:
- How is the combined mean of two groups calculated in general?
- What happens to the overall mean when the second group's mean is lower than the first?
- Can you derive the same result using a weighted average formula?
- How does the size of the groups affect the combined mean?
- What if there were more than two groups? How would the calculation change?
Tip: Always check if you can break down the problem into smaller parts (like totals) when dealing with means and averages.
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Math Problem Analysis
Mathematical Concepts
Mean (Rata-rata)
Algebra
Equation solving
Formulas
Mean formula: Mean = (Sum of all values) / (Number of values)
Equation: 30 * 7.7 + 5 * x = 35 * 8.0
Theorems
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Suitable Grade Level
Grade 8-9