How to find arithmetic mean
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PSAT Math › How to find arithmetic mean
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.
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 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
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.
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?
83
84
85
88
90
Explanation
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.
A, B, C, D, and E are integers such that A < B < C < D < E. If B is the average of A and C, and D is the average of C and E, what is the average of B and D?
(A + E)/2
(A + E)/4
(A + 2_C_ + E)/2
(A + 2_C_ + E)/4
(2_A_ + C + 2_E_)/2
Explanation
The average of two numbers can be calculated as the sum of those numbers divided by 2. B would thus be calculated as (A + C)/2, and D would be calculated as (C + E)/2. To find the average of those values, you would add them up and divide by 2:
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?
89
85
87
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.
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, 
What is the average (mean) of
Explanation
By adding all of the expressions we get
which averages to 
which will simplify to 