Finding an Average without the Individual Numbers
Date: 09/12/2006 at 15:15:58 From: Amanda Subject: Average score of all 50 students A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score of all 50 students who took the test? I don't know where to begin. It's hard to find the average when they don't give a set of numbers.
Date: 09/12/2006 at 16:03:51 From: Doctor Douglas Subject: Re: Average score of all 50 students Hi Amanda. It's true that they didn't give the entire slate of scores, but you still have enough information to find the average. The average score that you want is the total score of all the students divided by the total number of students. Clearly the total number of students is 50. Now, what about the total score? Can you figure out a way to obtain the total score of just the 35 juniors? It is possible to figure out this aggregate total without knowing all of the individual scores. If you are able to figure this out, I'm sure that you'll have no trouble finishing this problem. Write back if you get stuck. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
Date: 09/12/2006 at 16:39:16 From: Amanda Subject: Average score of all 50 students I took the total score of all the students, which was 80 + 70 = 150. I took this total of 150 and divided it by the total number of students which was 50 and I got 3. The average score of all 50 students is not 3, so I guess I need more help.
Date: 09/12/2006 at 16:53:01 From: Doctor Douglas Subject: Re: Average score of all 50 students Hi again, Amanda. Let's consider just the 35 juniors. How could they obtain an average score of 80? Well, one way is if they each scored exactly 80: 80 + 80 + ... + 80 = 35 x 80 = 2800. Another way is if one of them scored 2800 (because of a huge amount of extra credit) and everyone else scored zero--that would still lead to an average score of 80, because 2800/35 = 80. Either of these ways is certainly a possibility--all that matters is that the total score of the 35 juniors is 2800, so that the average score of the 35 juniors is 80. You want to find the total score of the seniors in a similar way, and add that to the total score of the juniors to get the total score of all 50 students. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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