# Averages

• Jul 18th 2009, 03:10 PM
A Beautiful Mind
Averages
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 for all 50 students who took the test?

Alright, apparently I was wrong...

I thought you'd take both of the averages of the two groups and then divide by two but apparently that's wrong.

70+80=150/2=75. The correct answer, it says, is 77.
• Jul 18th 2009, 03:22 PM
pomp
Quote:

Originally Posted by A Beautiful Mind
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 for all 50 students who took the test?

Alright, apparently I was wrong...

I thought you'd take both of the averages of the two groups and then divide by two but apparently that's wrong.

70+80=150/2=75. The correct answer, it says, is 77.

I can see why you would think to do it that way, but the correct way to calculate the average is total score/ total number of students.

So for the juniors, let $\displaystyle x$ be their total score. Then we know that $\displaystyle \frac{x}{35} = 80 ~ \Rightarrow ~ x = 2800$

For the seniors, let $\displaystyle y$ be their total score. Then similarly $\displaystyle \frac{y}{15} = 70 ~ \Rightarrow ~ y = 1050$

So the correct average for the 50 students as a whole is $\displaystyle \frac{x+y}{50} = \frac{3850}{50} = 77$
hope this helps,
pomp.
• Jul 18th 2009, 04:55 PM
A Beautiful Mind
Yeah, I just did it this way.

35/50 = 70% = 0.7
15/50 = 30% = 0.3

$\displaystyle = 0.7(80)+0.3(70)$

$\displaystyle = 56+21$

$\displaystyle = 77$
• Jul 18th 2009, 09:13 PM
matheagle
This is what you called a weighted average.
If the two sample sizes were equal, then you could just average the two averages.
• Jul 18th 2009, 09:34 PM
mr fantastic
Quote:

Originally Posted by A Beautiful Mind
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 for all 50 students who took the test?

Alright, apparently I was wrong...

I thought you'd take both of the averages of the two groups and then divide by two but apparently that's wrong.

70+80=150/2=75. The correct answer, it says, is 77.

If there was 4 students in one class (average mark 95%) and 400 students in the other class (average mark 25% - a large class of dopes) would you still be inclined to do it this way and say that the average score for all students was 60% ....
• Jul 18th 2009, 09:41 PM
A Beautiful Mind
No, of course not. I've just been accustomed to taking the arithmetic mean usually and I guess I was a little confused when it came to how it was 77.
• Jul 19th 2009, 04:37 AM
HallsofIvy
??? That is the arimetic mean!
• Jul 19th 2009, 06:46 AM
A Beautiful Mind
...what I was referring to was the idea of this:

I saw the averages of both at first and thought, hey, since they took the average of both of them maybe I can just put them together like you do with a group of test scores and then divide them by how many you have...

So I had 2 averages, added them together, and then divided by how many I had and that wasn't the case I figured out later on. I did before get the numbers in the thousands like in the first post but I wasn't sure you did it that way and just took the way I originally had and known to use all this time...

I got 75, which was surely an answer choice but not the right one.
• Jul 19th 2009, 08:43 AM
HallsofIvy
What you did was the arithmetic average of those two numbers. What the question was asking for was the arithmetic average of all 50 test scores.
• Jul 19th 2009, 06:50 PM
A Beautiful Mind
I know, I figured that out, lol.