Mrs. Gifford's class consists of 15 girls and 25 boys.
On the first test the mean of the girls’ scores was 80 and the mean of the boy’s scores was 70. What was the class mean? (Remember the class mean is not just averaging the two means)
mean = ∑x/n
Girl's 80 = ∑x/15
x = 1200
Boy's 70 = ∑x/25
x = 1750
Class mean = (1200+1750)/(15+25) = ?
(80*15 + 70*25)/(40)
To find the class mean, we need to calculate the overall average of all the students' scores in Mrs. Gifford's class. Here's how we can do it:
Step 1: Calculate the total score for the girls:
Since there are 15 girls and the mean of their scores is 80, the total score of all the girls together can be found by multiplying the mean (80) by the number of girls (15).
Total score of girls = Mean of girls × Number of girls
Total score of girls = 80 × 15
Total score of girls = 1200
Step 2: Calculate the total score for the boys:
Similarly, since there are 25 boys and the mean of their scores is 70, we can calculate the total score of all the boys by multiplying the mean (70) by the number of boys (25).
Total score of boys = Mean of boys × Number of boys
Total score of boys = 70 × 25
Total score of boys = 1750
Step 3: Calculate the total score of the class:
To find the class mean, we need to calculate the sum of the total scores of both the girls and boys.
Total score of the class = Total score of girls + Total score of boys
Total score of the class = 1200 + 1750
Total score of the class = 2950
Step 4: Calculate the class mean:
Finally, to find the class mean, we divide the total score of the class by the total number of students in the class, which is the sum of the number of girls and boys.
Class mean = Total score of the class ÷ Total number of students
Class mean = 2950 ÷ (Number of girls + Number of boys)
Class mean = 2950 ÷ (15 + 25)
Class mean = 2950 ÷ 40
Class mean = 73.75
Therefore, the class mean is 73.75.