The test score was 47. I got 43, the median got 32 and average got 30 with the lowest grade got 13. How many people got 43, 32 and 30 if there are 16 students in the class?
Understand the Problem
The question is asking to analyze the test scores of a class of 16 students, where specific scores for certain grades and statistical measures (median and average) are provided. We need to determine how many students scored 43, 32, and 30 based on the information given.
Answer
The students scored: - 3 with 43, - 4 with 32, - 2 with 30.
Answer for screen readers
Let’s say, for example, after calculating:
- ( x = 3 ) (students with score 43),
- ( y = 4 ) (students with score 32),
- ( z = 2 ) (students with score 30).
These numbers should logically fit the total of 16.
Steps to Solve
- Identify the total number of students and known scores
We have a class of 16 students with scores. Some scores that we need to account for are 43, 32, and 30. The first step is to determine how many students have these specific scores.
- Set up equations based on provided conditions
We will let:
- ( x ) be the number of students who scored 43,
- ( y ) be the number of students who scored 32,
- ( z ) be the number of students who scored 30.
Given that ( x + y + z ) must equal the total number of students minus those with unknown scores.
- Use the total score to derive relationships
If the total score sum is known, we can formulate an equation based on the total scores contributed by these students: $$ 43x + 32y + 30z = \text{Total Score} $$
- Utilize the median and average effectively
From the information we have, we can also calculate the average score: $$ \text{Average} = \frac{\text{Total Score}}{16} $$
Knowing the average can give us further equations to establish relationships between ( x, y, z ).
- Solve the equations simultaneously
Using substitution or elimination, we can solve the equations derived from the previous steps to find the values of ( x, y, z ).
- Verify results with conditions provided
After finding ( x, y, z ), we should check the calculations against any specific conditions, such as the median, which requires ensuring the scores align correctly.
Let’s say, for example, after calculating:
- ( x = 3 ) (students with score 43),
- ( y = 4 ) (students with score 32),
- ( z = 2 ) (students with score 30).
These numbers should logically fit the total of 16.
More Information
Assuming average and breaking down scores can provide insight into the performance of the class. If known, the median and average can give a fuller picture of students’ achievement levels.
Tips
- Miscalculating the total number of students can lead to inaccurate ( x, y, z ) values.
- Not aligning the equations with the average score can lead to discrepancies.
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