in an algebra class of 21 students the mean grade on a test was 87; in another class with 32 students the mean grade was 81. What is the combined mean of the two classed?
my teacher said it's 21 * 87 + 32 * 81/53= 83.4
but i'm not sure where the 53 came from..
thanks in advance
your adding the total number students from each class. 21 + 32 = 53
To find the combined mean of the two classes, you need to calculate the total sum of the grades and divide it by the total number of students.
Let's calculate it step by step:
1. Calculate the total sum of grades for each class:
- In the first class with 21 students, the mean grade is 87. So the total sum of grades for this class is 87 * 21 = 1827.
- In the second class with 32 students, the mean grade is 81. So the total sum of grades for this class is 81 * 32 = 2592.
2. Calculate the total number of students:
- The first class has 21 students.
- The second class has 32 students.
- So the total number of students is 21 + 32 = 53.
3. Calculate the combined mean:
- Add the total sum of grades for both classes: 1827 + 2592 = 4419.
- Divide the total sum of grades by the total number of students: 4419 / 53 = 83.4.
So, the combined mean grade of the two classes is indeed 83.4.
To find the combined mean of the two classes, you need to consider both the number of students and the average grades in each class.
Start by calculating the total score for each class:
- In the first class of 21 students, the mean grade is 87. So the total score for this class is 21 * 87.
- In the second class of 32 students, the mean grade is 81. So the total score for this class is 32 * 81.
Now, to find the combined mean, you need to add up the total scores of both classes and divide it by the total number of students.
The formula for the combined mean is:
Combined mean = (Total score of Class 1 + Total score of Class 2) / Total number of students
In this case, the formula can be expressed as:
Combined mean = (21 * 87 + 32 * 81) / (21 + 32)
To get the final answer, you need to evaluate the expression:
Combined mean = 1827 + 2592 / 53
The reason why the value of 53 appears in the formula is because it represents the total number of students in both classes combined. By adding the two class sizes together (21 + 32), you get 53.
Evaluating the expression gives:
Combined mean = 4419 / 53 ≈ 83.4
So, the combined mean grade of the two classes is approximately 83.4.