Step by step
The question
Question: A team of 12 players has a mean height of 75 inches.
Another team of 18 players has a mean height of 85 inches.
What is the mean height of all 30 players?
1 Total of each group
The first team has 12 players with a mean of 75.
Together they have 12 times 75.
That is 900.
The mean times how many numbers gives the total.
That is the key idea today.
The second team has 18 players with a mean of 85.
Together they have 18 times 85.
That is 1,530.
2 Put them together
All 30 players together: 900 plus 1,530 is 2,430.
And 12 plus 18 is 30 players.
Careful!
The two teams are not the same size.
So the mean of everyone is not halfway between 75 and 85.
3 Share equally
The mean shares the total equally: 2,430 divided by 30.
So the mean of all 30 players is 81.
4 Check
Let's check: if all 30 had 81, together they would have 81 times 30.
That is 2,430, the total.
So it is right!
And 81 is closer to 85, the mean of the bigger team.
That makes sense.
Let's look back.
First: total of each group.
Then: put them together.
Then: share equally.
Last: check.