Pre-calc Problem- See Details..............?

Question

9 Students took a test on time they recieved the folowing scores out of a possible 70 pnts. { 55, 70, 43, 68, 61, 48, 50, 68, 65}. GIve a possible scenerio where students who were absent made up the test and when there scores are added the following happens. 1.) Median Does Not Change. 2.) Mode Does Not Change. 3.) Median becomes EXACTLY 58. Thanks alot. Could you please explain the work.

Answer 1

Median is the average, so without knowing how many students were absent, we have to conclude the following:

1) if the median does not change, then the median score for those absent must still equal the median for those present. In other words, for each point above the median score an absent student scores, another student must score one point below the median score

2) mode is the most frequent number in a series. Since the mode in the present students is 68 (which occurs twice), we know that the scores of the absent students must still either have a mode of 68, or no mode at all with at least one 68

3) Currently we have a median of 58 2/3, so we need scores that will bring this median to exactly 58, which means the absent students must score slightly lower than the present students



Possible scenarios:

1) 3 absent students who score 58, 59, and 59
2) 3 absent students who score 58, 68, and 59
3) 3 absent students who score 50, 50, and 68

Answer 2

1) Just as many make-ups score below the median as above it.
2) 68 is still the most common score after their scores are included.
3) One scores 58, another 58, and one scores below 58.
Or one scores 59, one 57, and one below 57
etc.

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Hold on disposable!!! Median is NOT the same as average.