A teacher gives a test to a class of 20 student. Is it possible that 90% of the class scores above average? Give examples of test scores for which this is the case. If not, explain why not?
Of course it's possible. If 18 students get 100%, they all score above the average, which is less than 100.
Consider also negative scores, so if the two students achieves -100%, then everyone else only needs to achieve at least 2% to fit the conditions.
890
To determine whether it is possible for 90% of the class to score above average on a test, we need to understand how the average is calculated and the impact of individual test scores on the average.
First, let's discuss how to calculate the average. The average is obtained by summing up all the test scores and dividing by the total number of students. In this case, there are 20 students in the class.
Now, the average itself represents the summation of all test scores divided by the number of students. This means that the average score will depend on the individual scores of each student.
To determine if it is possible for 90% of the class to score above average, we need to consider the highest possible average score based on the available test scores. Since the average is obtained by dividing the sum of all test scores by the number of students, even if a large portion of the class scores above average, it is mathematically impossible for more than 50% of the class to score above average.
For example, let's assume the test scores are as follows:
Student 1: 80
Student 2: 80
Student 3: 80
...
Student 19: 80
Student 20: 100
In this case, the average score would be (80 * 19 + 100) / 20 = 81.5. We can see that even though 95% (19 out of 20) of the class scored above 81.5, it is impossible for 90% of the class to score above average.
In conclusion, it is not mathematically possible for 90% of the class to score above average.