Arithmetic Mean
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SAT Math › Arithmetic Mean
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 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 
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
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 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.
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.
The chart above lists the ages and heights of all the cousins in the Brenner family. What is the average age of the female Brenner cousins?
16.2
16.4
17.1
18.7
19.3
Explanation
There are five female cousins whose ages are 14, 22, 13, 12, and 20.
Add these up and divide by 5.
14 + 22 + 13 + 12 +20 = 81
81 / 5 = 16.2
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:
