Question 1132830: Hi again! The notes my professor gave me are sorta helpful but I’m no quite understanding it. The question is:
In a class of 24 students, if the mean on a 100 point test is 77, is it possible that 18 students got a score of 55 or below?
Thank you in advance :)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the class is 24 students.
if the mean is 77, then the total points scored by all students has to be 24 * 77 = 1848.
if 18 students got a score of 55 or below, the highest total points for the 18 students has to be 18 * 55 = 990.
1848 minus 990 = 858.
24 - 18 = 6.
that means that 6 students must have scored a total of 858 points or more.
858 / 6 = 143
that means the average score of the 6 students had to be 143.
since 100 is the highest score that any student can achieve, this is not possible.
not sure if this is what your teacher was trying to teach you, but this is how i looked at it.
i tried to look at it from a statistical standpoint, but i couldn't see how the standard deviation could be calculated since it doesn't appear that you have enough information to determine that.
if you send me the information your instructor gave you, i might be able to figure it out.
logically it makes sense that it's not possible, but that may not be the way your professor wanted you to solve it.
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