A teacher allows the students to each "throw out" their lowest test score in order to increase their
overall grade. The original mean score of 5 tests is 72.8. After the removal of the lowest test, the
mean score becomes 78.5. What is the score of the removed test?
A) 53 B) 50 C) 47 D) 51
5 * 72.8 = 364
78.5 * 4 = 314
364 - 314 = ?
To find the score of the removed test, we can use the concept of mean (or average) score.
Let's say the scores of the five tests are A, B, C, D, and E.
We know that the original mean score is 72.8. Therefore, the sum of the five scores is 5 × 72.8 = 364.
After removing the lowest test, the mean score becomes 78.5. Therefore, the sum of the four remaining scores is 4 × 78.5 = 314.
If we subtract the sum of the four remaining scores from the sum of the five original scores, we can find the score of the removed test.
364 - 314 = 50
So, the score of the removed test is 50.
The answer is option B) 50.
To find the score of the removed test, we can use the concept of the mean (average) score.
Let's denote the score of the removed test as "x".
Before removing the lowest test, the mean score of 5 tests is 72.8. This means that the sum of the scores of the 5 tests is 72.8 multiplied by 5. Therefore, the sum of the scores of the 5 tests is (72.8 * 5) = 364.
Now, let's calculate the sum of the scores of the remaining 4 tests after the removal of the lowest test. The mean score of the remaining 4 tests is 78.5. This means that the sum of the scores of the remaining 4 tests is 78.5 multiplied by 4. Therefore, the sum of the scores of the remaining 4 tests is (78.5 * 4) = 314.
We can now find the score of the removed test by subtracting the sum of the scores of the remaining 4 tests from the sum of the scores of the 5 tests:
Score of removed test = Sum of scores of 5 tests - Sum of scores of 4 tests
Score of removed test = 364 - 314
Score of removed test = 50
Therefore, the score of the removed test is 50.
Answer: B) 50