Your current exam mean is 93.2.If you receive an 87 on the next exam,this will have the effect of ______.
A)increasing your mean
B)decreasing your mean
C)having no effect on your mean
D)cannot determine

Question

Quizplus · Accepted Answer

To determine the effect of the 87 on your mean, you need to calculate the new mean.

Let's call the number of exams you've taken so far "n".

The current sum of your exam scores is: 93.2n

If you receive an 87 on the next exam, the new sum of your exam scores will be:

93.2n + 87

To find the new mean, you divide the new sum by the new number of exams (n+1, since you've taken one more exam):

(new sum) / (n+1) = (93.2n + 87) / (n+1)

Simplifying this expression gives:

(93.2n + 87) / (n+1) = (93.2n / (n+1)) + (87 / (n+1))

So, the new mean is a weighted average of your current mean (93.2) and the score you receive on the next exam (87), with more weight given to the current mean (since you've taken more exams already).

To determine whether the new mean will be higher or lower than 93.2, we need to compare it to 93.2:

If (93.2n / (n+1)) + (87 / (n+1)) > 93.2, then the new mean will be higher than 93.2.

If (93.2n / (n+1)) + (87 / (n+1)) < 93.2, then the new mean will be lower than 93.2.

If (93.2n / (n+1)) + (87 / (n+1)) = 93.2, then the new mean will be equal to 93.2.

To determine which of these is true, we need to know the value of n. Since n is not given, we cannot determine the answer with certainty.

However, we can make an educated guess based on common sense. If you've only taken one or two exams, then the effect of the 87 will be more noticeable, and the new mean will likely be lower than 93.2. If you've taken many exams, then the effect of the 87 will be less noticeable, and the new mean may be higher or lower than 93.2 depending on how you've been doing overall.

Therefore, the safest answer is B) decreasing your mean, since this is a likely outcome in many scenarios.

Your Current Exam Mean Is 93