Step by step
The question
Question: A class of 16 students has a mean score of 70.
A class of 24 students has a mean score of 80.
What is the mean score of all 40 students?
1 Total of each group
The first class has 16 students with a mean of 70.
Together they have 16 times 70.
That is 1,120.
The mean times how many numbers gives the total.
That is the key idea today.
The second class has 24 students with a mean of 80.
Together they have 24 times 80.
That is 1,920.
2 Put them together
All 40 students together: 1,120 plus 1,920 is 3,040.
And 16 plus 24 is 40 students.
Careful!
The two classes are not the same size.
So the mean of everyone is not halfway between 70 and 80.
3 Share equally
The mean shares the total equally: 3,040 divided by 40.
So the mean of all 40 students is 76.
4 Check
Let's check: if all 40 had 76, together they would have 76 times 40.
That is 3,040, the total.
So it is right!
And 76 is closer to 80, the mean of the bigger class.
That makes sense.
Let's look back.
First: total of each group.
Then: put them together.
Then: share equally.
Last: check.