Problem on Average?

Question

1 )Homer average 60 on quizzes in Math 13 and 70 the quizzes in Math 14. Yet his average of all his quizzes in Math 13 and 14 was not 65. How can that be?


2.) It is possible to have a class in which no student scores below the mean on the final exam. State precisely the conditions under which this can happen. Show that your answer is correct.
Please help me .I have no idea how to do this?

Answer 1

1)math 13,,and math 14,,
i didnt get what did u mean by that,,
but i think,,the number of quizzes in math 13 and math 14,,may not be the same,,

for eg,,
if there r 5 quizzes in math 13,,
the total score is,,60 into 5 = 300,,
and if there r 4 questions in math 14,,
the total score is,,70 into 4 = 280,,
thus,,
(280+300)divided by (5+4)
thats total average,,and is not necessarily be 65,,

2)theres one possibility,,
that all students got the same scores,,that is the mean score of the class,,

Answer 2

Question 1
This happens in either of the following cases:
1) The number of quizzes in Math 13 is not the same as the number of quizzes in Math 14
2) Not all quizzes have the same weight i.e. Some quizzes are granted more points than others

Question 2
As Previously suggested by the previous post

Answer 3

1) If there are a different number of quizzes in one class than another, his average will be higher or lower.

2) If all students score exactly the same then that score will be the mean, median and mode and nobody will score lower or higher.

Answer 4

I can only answer #2:

This can only happen if every student gets the same exact score (no matter what the number is) on the test, because then the mean would be that score and no one would be below it.