In a class of 20 students, the average (arithmetic mean) score on a test is 84 points. If 6 students each scored 100 points and 4 students each scored 50 points, what is the average of the scores of the remaining students?
average is 84, so the total is 20(84) or 1680 points
points of 6 students at 100 = 600
points of 4 students at 50 = 200
remaining points = 1680 - 600 - 200 = 880
average of those 10 students = 880/10 = 88
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To find the average score of the remaining students, we need to first calculate the total score of all the students who scored 100 points and those who scored 50 points:
Number of students who scored 100 points = 6
Number of students who scored 50 points = 4
Total score of students who scored 100 points = 6 * 100 = 600
Total score of students who scored 50 points = 4 * 50 = 200
Now, we can calculate the total score of all the students in the class:
Total score of all students = Number of students * Average score
Total score of all students = 20 * 84 = 1680
To find the total score of the remaining students, subtract the total score of the students who scored 100 or 50 points from the total score of all students:
Total score of remaining students = Total score of all students - Total score of students who scored 100 or 50 points
Total score of remaining students = 1680 - (600 + 200) = 880
Finally, we can calculate the average score of the remaining students:
Average score of remaining students = Total score of remaining students / Number of remaining students
Average score of remaining students = 880 / (20 - 6 - 4) = 880 / 10 = 88
Therefore, the average score of the remaining students is 88 points.
To find the average of the scores of the remaining students, we need to find the total sum of their scores and divide it by the number of remaining students.
First, let's find the total sum of the scores of all the students. We know that the average score of the entire class is 84 points, and there are 20 students. So, the total sum of scores can be calculated by multiplying the average score by the number of students: 84 x 20 = 1680.
Next, we need to subtract the scores of the 6 students who each scored 100 points and the 4 students who each scored 50 points.
The total sum of the scores of the 6 students who scored 100 points is 6 x 100 = 600 points.
The total sum of the scores of the 4 students who scored 50 points is 4 x 50 = 200 points.
To find the total sum of the scores of the remaining students, we subtract the sum of the scores of the students who scored 100 points and the sum of the scores of the students who scored 50 points from the total sum of scores: 1680 - 600 - 200 = 880 points.
Finally, we divide the total sum of the scores of the remaining students by the number of remaining students (20 - 6 - 4 = 10) to find their average score: 880 / 10 = 88.
Therefore, the average score of the remaining students is 88 points.