SOLUTION: I have a total number of 33 participants that took a survey. This is split into two groups. One group consisted of 22 people, the second group consisted of 11 people. I know the ov

Algebra ->  Average -> SOLUTION: I have a total number of 33 participants that took a survey. This is split into two groups. One group consisted of 22 people, the second group consisted of 11 people. I know the ov      Log On


   

Question 1014384: I have a total number of 33 participants that took a survey. This is split into two groups. One group consisted of 22 people, the second group consisted of 11 people. I know the overall approval percentage was 44%, the group consisting of 22 people averaged 36%, how do I find out what the score was for the other group of 11 people to get to the final approval percentage of 44?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
22 * 36% + 11 * x = 33 * 44%

simplify to get 792% + 11x = 1452%

subtract 792% from both sides of the eqaution to get:

11x = 1452% - 792%

simplify to get 11x = 660%

sivide both sides of this equation by 11 to get x = 660/11 = 60%

the first group averaged 36%.

the second group averaged 60%.

basically, the formula is:

total score / number of people = average score per person.

average score per person * number of people = total score.

22 * 36% + 11 * 60% = 1452% / 33 = 44% per person.

44% is your overall average.

the average for the group of 22 is 36%
the average for the group of 11 is 60%.

you could also look at it in the following way.

22 / 33 = 2/3 of the total group.
11 / 33 = 1/3 of the total group.

your overall weighted average is equal to 2/3 * 36% + 1/3 * 60% = 44%.