SOLUTION: In psychology class, 43 students have a mean score of 87.8 on a test. Then 9 more students take the test and their mean score is 77. What is the mean score of all the students to

Question 1182123: In psychology class, 43 students have a mean score of 87.8 on a test.
Then 9 more students take the test and their mean score is 77.
What is the mean score of all the students together?
Round to one decimal point.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The first 43 students have a mean of 87.8

Recall that the process of finding the mean involves two basic steps
A) add up the numbers
B) divide by n, which is the number of items in the set

When we apply step A, we'll get a sum S
Dividing S over n gets us the mean
S/n = mean
S/43 = 87.8
S = 87.8*43
S = 3,775.4
This is the sum of the first 43 students' scores.

Repeat this process for the other extra 9 students
R = 77*9
R = 693
This is the sum of the extra 9 scores.

In total, all of the scores add to S+R = 3,775.4+693 = 4,468.4

The last thing to do is to divide that total sum by 43+9 = 52, as this is the total number of people in the class.

mean score of everyone = (total of all the scores)/(total number of students)
mean score of everyone = (4,468.4)/(52)
mean score of everyone = 85.9307692307692
mean score of everyone = 85.9

As you can see, these type of problems involve determining the sum so then you can then follow the steps mentioned earlier (step A and step B).

Notice how the final answer is closer to the first groups' mean instead of the second group. The first group being the 43 people of course. This occurs because the first group has more people in it, and therefore they apply more weight. Think of it like a tug-of-war. The first group has more pull toward it to make the mean be closer to 87.8 rather than be closer to 77.

Answer: 85.9

Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

The total of the 43 students is 43*87.8 scores. The total of the 9 students is 9*77 scores. The grand total is 43*87.8 + 9*77. The mean score for the entire class of 43 + 9 students is = 85.9 (rounded) ANSWER

Solved.

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