A class of 30 students has a mean score of 88. A class of 20… Step by Step

Step by step

The question

Question: A class of 30 students has a mean score of 88.

A class of 20 students has a mean score of 78.

What is the mean score of all 50 students?

1 Total of each group

The first class has 30 students with a mean of 88.

Together they have 30 times 88.

That is 2,640.

class 1 total = 30 × 88 = 2,640

The mean times how many numbers gives the total.

That is the key idea today.

mean × how many = total

The second class has 20 students with a mean of 78.

Together they have 20 times 78.

That is 1,560.

class 2 total = 20 × 78 = 1,560

2 Put them together

All 50 students together: 2,640 plus 1,560 is 4,200.

total = 2,640 + 1,560 = 4,200

And 30 plus 20 is 50 students.

how many = 30 + 20 = 50

Careful!

The two classes are not the same size.

So the mean of everyone is not halfway between 88 and 78.

Careful: not (88 + 78) ÷ 2 = 83 ✗

3 Share equally

The mean shares the total equally: 4,200 divided by 50.

mean = 4,20050

So the mean of all 50 students is 84.

mean = 84

4 Check

Let's check: if all 50 had 84, together they would have 84 times 50.

That is 4,200, the total.

So it is right!

84 × 50 = 4,200

And 84 is closer to 88, 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.

Answer