How to find arithmetic mean
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SAT Math › How to find arithmetic mean
A police officer walked into a room full of suspects and turn out their pockets. The chart below shows the number of coins each man had.
The police claim the man with the amount of money closest to the arithmetic mean of the group is guilty. Who is it?
Suspect 2
Suspect 1
Suspect 3
Suspect 4
Suspect 6
Explanation
Summing total money and dividing by the number of suspects gives us an average of approximately $2.73. By comparing it to the amounts held by the suspects, we can see that Suspect #2 is guilty.
If Billy has an average of 
Explanation
In order to solve this lets write two general equations that we will solve.
From the first equation, we get.
Substitute tis into the next equation,
Solve for 
If the average of 5k and 3l is equal to 50% of 6l, what is the value of k/l ?
3/5
5/3
9/5
5/9
Explanation
Since the first part of the equation is the average of 5k and 3l, and there’s two terms, we put 5k plus 3l over 2. This equals 50% of 4l, so we put 6l over 2 so they have common denominators. We can then set 5k+3l equal to 6l. Next, we subtract the 3l on the left from the 6l on the right, giving us 5k=3l. To get the value of k divided by l, we divide 3l by 5, giving us k= 3/5 l. Last we divide by l, to give us our answer 3/5.
This semester, Mary had five quizzes that were each worth 10% of her grade. She scored 89, 74, 84, 92, and 90 on those five quizzes. Mary also scored a 92 on her midterm that was worth 25% of her grade, and a 91 on her final that was also worth 25% of her class grade. What was Mary's final grade in the class?
85
87
89
91
93
Explanation
To find her average grade for the class, we need to multiply Mary's test scores by their corresponding weights and then add them up.
The five quizzes were each worth 10%, or 0.1, of her grade, and the midterm and final were both worth 25%, or 0.25.
average = (0.1 * 89) + (0.1 * 74) + (0.1 * 84) + (0.1 * 92) + (0.1 * 90) + (0.25 * 92) + (0.25 * 91) = 88.95 = 89.
Looking at the answer choices, they are all spaced 2 percentage points apart, so clearly the closest answer choice to 88.95 is 89.
If Mary traveled 116 miles on day 1, 130 miles on day 2, 114 miles on day 3. How many miles per day did she average?
114
115
116
118
120
Explanation
To find an average you add all the values and divide by the number of values. 116+114+130 = 360. 360/3 = 120
If the mean of z and s is 22, and the mean of b and f is 22, what is the mean of z, s, b, and f?
22
17
20
27
Explanation
If the average of two numbers is 22, and the average of two more numbers is 22, the average of all of them will be 22.
The mean of 12, 14, 18, 20, and x is equal to 14. Solve for x.
6
12
14
20
5
Explanation
- Set up an equation to find the mean (or average) of the series of numbers. (x + 64)/5 = 14 (64 = 12 + 14 + 18 + 20)
- In order to solve for x, first multiply both sides by 5
- x + 64 = 70
- Subtract 64 from both sides.
- x = 6.
A class has test results of 98, 86, 72, 88, and 92. What score does Angie have to get on the test in order to make the average a 85?
60
63
74
87.2
90
Explanation
With Angie's score there will be 6 total scores. 60*85(the average) gives a sum of scores as 510. Subtracting the scores of the other students gives a difference of 74. This means that Angie must score a 74 to have the class average be 85.
The mean of a series of 6 numbers (11, 12, 14, 17, 18, x) is 15. Solve for x.
18
19
17
16
Explanation
If the mean of 6 numbers is 15, that implies that the sum of the numbers is equal to 90 (6 x 15).
Therefore, 
The average for 24 students on a test is 81%. Two more students take the test, averaging 74% between the two of them. What is the total class average (to the closest hundreth) if these two students are added to the 24?
77.5%
77.44%
79.12%
81.22%
80.46%
Explanation
The easiest way to solve this is to consider the total scores as follows:
Group 1: 81 * 24 = 1944
Group 2: 74 * 2 = 148
Therefore, the total percentage points earned for the class is 148 + 1944 = 2092. The new class average will be 2092/26 or 80.46. (For our purposes, this is 80.46%.)