# Arithmetic Mean

These lessons, with videos, examples and step-by-step solutions help SAT students to review arithmetic mean or average.

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The following diagram shows how to find the arithmetic mean or average. Scroll down the page for more examples and solutions on arithmetic mean or average. How to find the arithmetic mean or average?

1. Add up all the numbers.
2. Divide the total by how many there are.

Solving Math Problems : Finding the Mean
In math, the mean is found by adding pieces of data together and dividing by the number of pieces of data.

Example:
Find the mean of 2, 8, 13, 4, 21, 18

SAT Math - Averages (Arithmetic Mean)
This is an averages problem from the SAT online study course, practice test #1, section 4, problem 18.

Example:
The average (arithmetic mean) of 3 numbers is x. If one of the numbers is y, what is the average of the remaining 2 numbers in terms of x and y?
(A) x/3
(B) (2y - x)/3
(C) (2x - y)/3
(D) (3y - x)/2
(E) (3x - y/2

SAT Math Review: Arithmetic Mean (Average)

Example:
If a = 3b = 6c, what is the average (arithmetic mean) of a, b, and c in terms of a?

SAT Math Lesson: Arithmetic Mean

SAT Math - Averages
Example:
108. Lisa took four chemistry exams and received an average score of 82. If she scores a 97 on her next chemistry exam, what will be her average for all five exams?
109. Gerald’s average score for nine tests was 96. If the sum of the scores of two of his tests was 178, then what was his average for the other seven tests?
110. If the average of eight numbers is 46 and the average of three of these is 51, what is the average of the other five numbers?
111. There are 7 numbers in set X. The average of the first 2 numbers is 79 and the sum of the last 5 numbers is 290. What is the average of all 7 numbers in set X?
112. The average of a list of 5 numbers is y. When an additional number is added to the list, the average of all numbers is y + 3. Which of the following is the value of the number added to the list in terms of y?

Example:

1. The average of y and 3 is equal to the average of y, 4 and 6. Find y.
2. The average of four numbers is 15. If three of those numbers are 7, 9 and 16, find the last number.
3. The average of 13, 15 and 17 is 10 more than the average of 4 and what number?
4. The average height of South College’s student body is 5 foot 6 inches. If the 2000 women at the college average 5 foot 4 inches, what is the average height of the 1800 men at the college?
5. The average (arithmetic mean) of a, b and c is 24. The sum of a and twice the value of c is 26. What is a + 2b equal to?
6. After a basketball game involving m players, n is the sum of all the points scored by every player in the game. What expression is equal to the average number of points scored by a player in the game?
7. A lab technician is recording sample sizes, and ‘a’ stands for the average sample size. If b is the total number of samples, what expression is equal to the total sum of all of the sample sizes?
8. Kelly went to the gym for x hours on Monday, for twice as many hours on Tuesday, and for half as many hours on Wednesday, What’s an expression that’s equal to the average number of hours Kelly spent in the gym over the three days?
9. The average temperature over a 10-day period was 88 degrees. For the first six days, it was sunny, and the average temperature was 90 degrees. Over the next 4 days, it rained, and the temperature dropped. What was the average temperature for those 4 days?
10. P is a set of numbers with an average (arithmetic mean) of 5. Q is a set of numbers found by subtracting 3 from each of the numbers in set P. What is the average of the numbers in set Q?
11. 5 consecutive integers have an average of 125. What’s the average of the first three of those integers?
12. 7 consecutive even integer have an average of 56. Find the average of the greatest two of those integers.
13. The average of 4 consecutive even integers is 11. Find the average of the first two of those integers.

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