The mean grade of the 30 students in section 1 is 80. the mean grade of the 40 students in section 2 is 85. the mean grade of the 30 students in section 3 is 80. what is the mean grade of all students from the three sections combined?

You can't simply consider the mean of the three means, because each mean is achieved by a different number of students.

Consider an extreme example, just to understand the concept: if 1 students gets a grade of 100 and one million students get a grade of 0, we can't say that the combined mean is 50!

What we need to do is called a weighted average, i.e. an average where we consider the weight of every entry - in this case the weight is given by how many students achieved a certain grade.

So, if each value comes with a weight , the weighted average is computed as

Applying this formula to your case, we have

b

step-by-step explanation: