This is a mean with percentage problem...

Mr. Ramirez and Ms. Jonsey gave tests to their classes with the results seen in the table.

	Overall Mean	Mean for Females	Mean for Males	Percent Females
Ramirez	218	230	205
Jonsey	221	224		88

What are the missing entries? For an overall mean, Ms. Jonsey’s class is higher, but for females, the mean is higher in Mr. Ramirez’s class. Is it possible that the mean for males is higher in Mr. Ramirez’s class as well?

The hint they give me is:
To find the entry for the empty cell in the bottom row, consider the remaining percentage for Ms. Jonsey's class and how that percentage was used to determine the overall mean. For the missing entry in Mr. Ramirez's class, think algebraically about the conditions on the total percentages and how those percentages were used to obtain the overall mean for his class.

I think the means for Males in Ms. Jonsey's class is 218, but I am not sure. My professor has not answered emails and I am stuck. Can anyone please help me in understanding this problem?

Thank you in advance and I really appreciate the help I receive.

Schuyla

This looks tricky, the only way I can find a result for that bottom cell is using a weighted mean (don't think that equals the overall mean in this case)

88% female implies 12% male and thus

how did you get the 211?

I think 211 is a typo for 221

For the Ramirez group, suppose that there are females and males.
The total score for the females will be and for the males leading to an overall mean of

Put this equal to and simplify to arrive at
The percentage number of females in the group will be and on substituting this works out at

For the Jonsey group you have to work this calculation in reverse, that is, start with the percentage number of females and then move on to the overall mean.

Thank you to both of you for your help! I now understand how to solve this problem.

Let f be the number of females in the class, m the number of males, A the "mean for females" and B the "mean for males".
The total scores for females is Af and the total score for males is Bm. The total of all scores is Af+ Bm. The overall mean, then, is . Of course, those two fractions are "the percent of females" and "the percent of males": the overall mean is "mean for females times percentage of females"+ "mean for males times percentage of males".

Here's how I would have done the first problem: Let p= "percentage of females" (in the class). Then the percentage of males is 1- p so the overall mean grade is p(230)+ (1- p)(205)= 218. Solve that equation of p.

For the second use the same formula: let m be the mean for males in the class. The females form 88% of the class so males constitute 12% of it. We must have .88(224)+ .12m= 221. Solve that for m.