Step by step
The question
Question: A class of 20 students has a mean score of 80.
A class of 30 students has a mean score of 70.
What is the mean score of all 50 students?
1 Total of each group
The first class has 20 students with a mean of 80.
Together they have 20 times 80.
That is 1,600.
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 50 students together: 1,600 plus 2,100 is 3,700.
And 20 plus 30 is 50 students.
Careful!
The two classes are not the same size.
So the mean of everyone is not halfway between 80 and 70.
3 Share equally
The mean shares the total equally: 3,700 divided by 50.
So the mean of all 50 students is 74.
4 Check
Let's check: if all 50 had 74, together they would have 74 times 50.
That is 3,700, the total.
So it is right!
And 74 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.