Step by step
The question
Question: A class of 40 students has a mean score of 62.
A class of 10 students has a mean score of 72.
What is the mean score of all 50 students?
1 Total of each group
The first class has 40 students with a mean of 62.
Together they have 40 times 62.
That is 2,480.
The mean times how many numbers gives the total.
That is the key idea today.
The second class has 10 students with a mean of 72.
Together they have 10 times 72.
That is 720.
2 Put them together
All 50 students together: 2,480 plus 720 is 3,200.
And 40 plus 10 is 50 students.
Careful!
The two classes are not the same size.
So the mean of everyone is not halfway between 62 and 72.
3 Share equally
The mean shares the total equally: 3,200 divided by 50.
So the mean of all 50 students is 64.
4 Check
Let's check: if all 50 had 64, together they would have 64 times 50.
That is 3,200, the total.
So it is right!
And 64 is closer to 62, 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.