Finding the combined mean of two groups with different sizes

[Dollydaggerxo]

Homework Statement

I realize this is probably an obvious question, but if there are two groups, say group A and group B, where group A was full of old people, and group B full of children.
The mean age was 67 for group A
and the mean age was 5 for group B.
If these two groups joined together to make one big group, what is the new mean?

The Attempt at a Solution

is it just ( 67 + 5 ) / 2
so it would be 36?

 

[dacruick]

yes assuming groups A and B are the same size.

 

[Dollydaggerxo]

Oh i see, so what happens if they are different sizes?

say A is 4 ad B is 5.

 

[dacruick]

well then that is what is called different weighting. For example, take your grades. if you had two tests both worth 50% of your mark. They are weighted the same. If you get 70% on one and 80% on the other, your average will be (70+80)/2.

however if one is worth 25% and one is worth 75%, and you got the same marks respectively, your final mark would be 0.25(70) + 0.75(80)

 

[dacruick]

and if you don't see the mathematic pattern; (70+80)/2 is exactly the same as 0.5(70)+0.5(80)

 

[Dollydaggerxo]

ah brilliant, I never thought of it like that!
Thankyou

 

[dacruick]

Yes, everything is simple once you understand it. This same concept is applied on the periodic table. I don't know how well you know chemistry, but you must know that each different element has an atomic weight. You also might know of isotopes. Carbon is the atomic number 12 on the periodic table which means that it has 12 protons. But there are also isotopes of carbon such as carbon 13(which has 13 protons). So from the samples scientists see that 3% of the chunk of carbon is carbon 13, and 90% is carbon 12, and 7% is carbon 11. Then the weight that shows up on your periodic table is as follows:

0.03(weight of carbon 13) + 0.90(weight of carbon 12) + 0.07(weight of carbon 11)

 

[Dickfore]

Yes, everything is simple once you understand it. This same concept is applied on the periodic table. I don't know how well you know chemistry, but you must know that each different element has an atomic weight. You also might know of isotopes. Carbon is the atomic number 12 on the periodic table which means that it has 12 protons. But there are also isotopes of carbon such as carbon 13(which has 13 protons). So from the samples scientists see that 3% of the chunk of carbon is carbon 13, and 90% is carbon 12, and 7% is carbon 11. Then the weight that shows up on your periodic table is as follows:

0.03(weight of carbon 13) + 0.90(weight of carbon 12) + 0.07(weight of carbon 11)

All isotopes of carbon have 6 protons. You clearly do not understand the periodic table.

 

[dacruick]

All isotopes of carbon have 6 protons. You clearly do not understand the periodic table.

haha i clearly meant 13 protons and neutrons. but who cares this is a physics forum. tehre was no issue insofar as the concept explained. what are you being a dickfor?

 

[jeppetrost]

Is it only me, who saw the kinda joke..? "What are you being a dick for, Dickfore?"