PSAT Math : How to find arithmetic mean
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Example Question #51 : How To Find Arithmetic Mean
The average of 12, 11, 10, 16, and x is 12. Solve for x.
9
11
12
13
10
11
The average is the sum of the numbers divided by the total number of terms. Therefore, 
We can multiply each side by 5 leaving us with 
We can simplify this equation to 
After subtracting 49 from both sides, we are left with 
Example Question #52 : How To Find Arithmetic Mean
A certain group of 12 students has an average age of 17. Two new students enter the group. The average age of the group goes up to 18. What is the average age of the two new students that came in?
20
12
28
24
16
24
If 12 students have an average age of 17, we can say 
Therefore the sum of the students' ages is 12 x 17 = 204.
Two students enter the group, so the total number of students goes up to 14.
We are told that the new average age is 18.
Thus, the sum of the ages of the 14 students is 14 x 18 = 252.
The difference of the two sums gives us the sum of the ages of the two new students:
252 - 204 = 48
The average age of the two new students is then 48/2 = 24.
Example Question #53 : How To Find Arithmetic Mean
On her first four math tests, Kelly earned scores of 75, 85, 92, and 80. What must she score on the fifth test to make her class average 84?
85
90
88
83
84
88
The average of five tests scores must be 84. In other words, (sum of five scores)/5 = 84.
Let's multiply both sides by 5:
sum of five scores = 420
The sum of the first four scores plus the fifth score must be 420. The sum of the first four scores is 75 + 85 + 92 + 80 = 332.
Therefore, 332 + fifth score = 420.
Subtract 332 from both sides:
fifth score = 88.
The answer is 88.
Example Question #51 : Statistics
A group of four students took a test. The average of their scores was 86. Two students scored 82 on the test. What was the average score of the two other students?
We know the average test score was 86, and that the average is the sum of the scores of the students who took the test divided by the number of students.
To find the sum of the scores on the test, multiply the average score by 4:
The four students scored a total of 344 points on the test. To find the average of the students' scores we don't know, subtract the students' scores we do know from the sum:
The two students whose scores we do not know scored a combined 180 on the test. To find their average score, divide by the number of students whose score we do not know. We are only looking for the average, so their individual scores are not important.
The average score of the two students whose score we do not know is 90.
Example Question #54 : How To Find Arithmetic Mean
On his first three statistics tests, Abe has scored 73, 82, and 75. What must he score on the fourth test to bring his average to exactly 80?
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