To solve this problem, we need to first find the median score of the original 7 tests.
Arranging the scores in order:
68, 68, 73, 83, 94, 100
The median score is 83.
Since the median score increased by 2 points after adding the 2 new test scores, the new median score must be 85.
We can add the 2 new test scores (let's call them x and y) to the original scores and find the new median:
68, 68, 73, 83, 94, 100, x, y
To find the new median, we need to find the middle two numbers since there are now 8 scores.
The middle two numbers are the original 83 and the new median of 85.
So, we can set up an equation:
(83 + 85) / 2 = (68 + 68 + 73 + 83 + 94 + 100 + x + y) / 8
Simplifying this equation:
84 = (536 + x + y) / 8
672 = 536 + x + y
x + y = 136
We also know that the mean (average) of the 9 scores is the same as the mean of the original 7 scores.
The sum of the original 7 scores is:
68 + 68 + 73 + 83 + 94 + 100 + 68 = 554
The sum of all 9 scores is:
68 + 68 + 73 + 83 + 94 + 100 + x + y + 100 = 686 + x + y
We can set up another equation:
(686 + x + y) / 9 = 554 / 7
Simplifying:
686 + x + y = 791.43
x + y = 105.43
Now we have two equations:
x + y = 136
x + y = 105.43
Subtracting the second equation from the first:
x + y - x - y = 136 - 105.43
0 = 30.57
This is impossible, so our original assumption (that the median increased by 2 points after adding two 100-point tests) must be incorrect.
Therefore, there is no solution to this problem.
94, 73, 68, 83, 100, 68, these are the test scores.
The student takes 2 more 100 point tests Before the grading period closes. The addition of these 2 test scores has no effect on the mean, but the median score of all the tests increased by 2 points. What was the scores of the 2 most recent tests?
1 answer