Step by step
The question
Question: A class of 10 students has a mean score of 90.
A class of 30 students has a mean score of 70.
What is the mean score of all 40 students?
1 Total of each group
The first class has 10 students with a mean of 90.
Together they have 10 times 90.
That is 900.
The mean times how many numbers gives the total.
That is the key idea today.
The second class has 30 students with a mean of 70.
Together they have 30 times 70.
That is 2,100.
2 Put them together
All 40 students together: 900 plus 2,100 is 3,000.
And 10 plus 30 is 40 students.
Careful!
The two classes are not the same size.
So the mean of everyone is not halfway between 90 and 70.
3 Share equally
The mean shares the total equally: 3,000 divided by 40.
So the mean of all 40 students is 75.
4 Check
Let's check: if all 40 had 75, together they would have 75 times 40.
That is 3,000, the total.
So it is right!
And 75 is closer to 70, 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.