Arithmetic Mean - SAT Math
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If the average of 5k and 3l is equal to 50% of 6l, what is the value of k/l ?
If the average of 5k and 3l is equal to 50% of 6l, what is the value of k/l ?
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.
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.
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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?
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?
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.
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.
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The St. Louis area has the following weather:
Monday High Temperature 76 Low Temperature 51
Tuesday High Temperature 82 Low Temperature 62
Wednesday High Temperature 67 Low Temperature 37
What is the difference between the high temperature average and the low temperature average over the three days?
The St. Louis area has the following weather:
Monday High Temperature 76 Low Temperature 51
Tuesday High Temperature 82 Low Temperature 62
Wednesday High Temperature 67 Low Temperature 37
What is the difference between the high temperature average and the low temperature average over the three days?
Average = sum of data points ÷ number of data points
High temperature average = (76 + 82 + 67) ÷ 3 = 75
Low temperature average = (51 + 62 + 37) ÷ 3 = 50
The difference between the two averages is 25.
Average = sum of data points ÷ number of data points
High temperature average = (76 + 82 + 67) ÷ 3 = 75
Low temperature average = (51 + 62 + 37) ÷ 3 = 50
The difference between the two averages is 25.
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In the following set of numbers, the arithmetic mean exceeds the mode by how much?
{2, 2, 4, 8, 10, 12, 20, 30}
In the following set of numbers, the arithmetic mean exceeds the mode by how much?
{2, 2, 4, 8, 10, 12, 20, 30}
The arithmetic mean is defined as:
The sum of a list of values divided by the number of values in the list.
Therefore for this problem, the arithmetic mean is:
(2+2+4+8+10+12+20+30) / 8 = (88/8) = 11
The mode is defined as the value that occurs the greatest number of times in a list of values.
In this case, it would be 2.
Therefore, the arithmetic mean (11) exceeds the mode (2) by 9.
The arithmetic mean is defined as:
The sum of a list of values divided by the number of values in the list.
Therefore for this problem, the arithmetic mean is:
(2+2+4+8+10+12+20+30) / 8 = (88/8) = 11
The mode is defined as the value that occurs the greatest number of times in a list of values.
In this case, it would be 2.
Therefore, the arithmetic mean (11) exceeds the mode (2) by 9.
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The average age of a certain group of 20 people is 25 years old. Another group of 10 people with an average age of 40 years comes in and joins the first group. What is the average age of the new group?
The average age of a certain group of 20 people is 25 years old. Another group of 10 people with an average age of 40 years comes in and joins the first group. What is the average age of the new group?
We cannot just take the average of the ages 25 and 40, which is 32.5 years old.
Instead, we need to take a weighted average, taking into account the varying number of people in each group.
Take the average age of each group and multiply it by the number of people in that group and then take the sum. Next divide by the total number of people to get the weighted average age of the new group.
(20 * 25 + 10 * 40)/30 = 30
We cannot just take the average of the ages 25 and 40, which is 32.5 years old.
Instead, we need to take a weighted average, taking into account the varying number of people in each group.
Take the average age of each group and multiply it by the number of people in that group and then take the sum. Next divide by the total number of people to get the weighted average age of the new group.
(20 * 25 + 10 * 40)/30 = 30
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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?
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?
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%.)
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%.)
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Twenty students scored an average of 83% on a test. After three more took the exam, the class average was exactly 84%. Which of the following is a possible set of scores for these three students?
Twenty students scored an average of 83% on a test. After three more took the exam, the class average was exactly 84%. Which of the following is a possible set of scores for these three students?
Let's think of the exams in terms of 100 points for a 100%. This means that the first 20 students received 20 * 83 or 1660 points.
Now, we must figure out how many points would be necessary for 23 students to have an average of exactly 84%. That would be found using the equation for a mean:
x / 23 = 84 → x = 1932
That means that our 3 students had to get a total of 1932 – 1660, or 272 points. The only answer that matches that among our answers is 84%, 92%, and 96%.
Let's think of the exams in terms of 100 points for a 100%. This means that the first 20 students received 20 * 83 or 1660 points.
Now, we must figure out how many points would be necessary for 23 students to have an average of exactly 84%. That would be found using the equation for a mean:
x / 23 = 84 → x = 1932
That means that our 3 students had to get a total of 1932 – 1660, or 272 points. The only answer that matches that among our answers is 84%, 92%, and 96%.
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If a = 2b = 4c = 8d, what is the average of a, b, c, and d, in terms of a?
If a = 2b = 4c = 8d, what is the average of a, b, c, and d, in terms of a?
Convert each term, so a = a, b = a/2, c = a/4, and d = a/8
so then the average would be (a + a/2 + a/4 + a/8)/4
= (8a/8 + 4a/8 + 2a/8 + a/8)/4
= (15a/8)/4 = 15a/32
Convert each term, so a = a, b = a/2, c = a/4, and d = a/8
so then the average would be (a + a/2 + a/4 + a/8)/4
= (8a/8 + 4a/8 + 2a/8 + a/8)/4
= (15a/8)/4 = 15a/32
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Daria plays darts often. She scores 25 points 1/5 of the time she plays. She also scores 50 points with probability 3/5, and 0 points with probability 1/5. What is the average number of points Daria scores when she plays darts?
Daria plays darts often. She scores 25 points 1/5 of the time she plays. She also scores 50 points with probability 3/5, and 0 points with probability 1/5. What is the average number of points Daria scores when she plays darts?
To find the average number of points, we need to multiply the points by their corresponding weights and sum them up.
Average = 1/5 * 25 + 3/5 * 50 + 1/5 * 0 = 35.
To find the average number of points, we need to multiply the points by their corresponding weights and sum them up.
Average = 1/5 * 25 + 3/5 * 50 + 1/5 * 0 = 35.
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What is the arithmetic mean of all of the odd numbers between 7 and 21, inclusive?
What is the arithmetic mean of all of the odd numbers between 7 and 21, inclusive?
One can simply add all the odd numbers from 7 to 21 and divide by the number of odd numbers there are. Or, moreover, one can see that 14 is halfway between 7 and 21.
One can simply add all the odd numbers from 7 to 21 and divide by the number of odd numbers there are. Or, moreover, one can see that 14 is halfway between 7 and 21.
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It takes Johnny 25 minutes to run a loop around the track. He runs a second loop and it takes him 30 minutes. If the track is 5.5 miles long, what is his average speed in miles per hour?
It takes Johnny 25 minutes to run a loop around the track. He runs a second loop and it takes him 30 minutes. If the track is 5.5 miles long, what is his average speed in miles per hour?
The minutes must be converted to hours which gives 11/12 hours. The total distance he runs is 11 miles. 11/(11/12) = 12.
The minutes must be converted to hours which gives 11/12 hours. The total distance he runs is 11 miles. 11/(11/12) = 12.
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I recently joined a bowling team. Each night we play three games. During my first two games I scored a 112 and 134, what must I score on my next game to ensure my average for that night will be a 132?
I recently joined a bowling team. Each night we play three games. During my first two games I scored a 112 and 134, what must I score on my next game to ensure my average for that night will be a 132?
To find the average you add all the games and divide by the number of games. In this case we have 112 + 134 + x = 246 + x. If we divide by 3 and set our answer to 132, we can solve for x by cross multiplying and solving algebraically. We can also solve this problem using substitution.
To find the average you add all the games and divide by the number of games. In this case we have 112 + 134 + x = 246 + x. If we divide by 3 and set our answer to 132, we can solve for x by cross multiplying and solving algebraically. We can also solve this problem using substitution.
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For the fall semester, three quizzes were given, a mid-term exam, and a final exam. To determine a final grade, the mid-term was worth three times as much as a quiz and the final was worth five times as much as a quiz. If Jonuse scored 85, 72 and 81 on the quizzes, 79 on the mid-term and 92 on the final exam, what was his average for the course?
For the fall semester, three quizzes were given, a mid-term exam, and a final exam. To determine a final grade, the mid-term was worth three times as much as a quiz and the final was worth five times as much as a quiz. If Jonuse scored 85, 72 and 81 on the quizzes, 79 on the mid-term and 92 on the final exam, what was his average for the course?
The formula for a weighted average is the sum of the weight x values divided by the sum of the weights. Thus, for the above situation:
Average = (1 x 85 + 1 x 72 + 1 x 81 + 3 x 79 + 5 x 92) / ( 1 + 1 + 1 + 3 + 5)
= 935 / 11 = 85.
The formula for a weighted average is the sum of the weight x values divided by the sum of the weights. Thus, for the above situation:
Average = (1 x 85 + 1 x 72 + 1 x 81 + 3 x 79 + 5 x 92) / ( 1 + 1 + 1 + 3 + 5)
= 935 / 11 = 85.
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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, 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?
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:
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:
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The average (arithmetic mean) of m, n and p is 8. If m + n = 15 then p equals:
The average (arithmetic mean) of m, n and p is 8. If m + n = 15 then p equals:
If the arithmetic mean of the three numbers is 8, then the three numbers total 24. We are given m + n, leaving p to equal 24 – 15 = 9.
If the arithmetic mean of the three numbers is 8, then the three numbers total 24. We are given m + n, leaving p to equal 24 – 15 = 9.
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Susie drove 100 miles in 2 hours. She then traveled 40 miles per hour for the next hour, at which point she reached her destination. What was her average speed for the entire trip?
Susie drove 100 miles in 2 hours. She then traveled 40 miles per hour for the next hour, at which point she reached her destination. What was her average speed for the entire trip?
Distance = Rate * Time
We are solving for the rate. Susie was driving for a total of 3 hours. The distance she traveled was 100 miles in the first leg, plus 40 miles (40 miles per hour for one hour) in the second leg, or 140 miles total. Use the total distance and total time to solve for the rate.
140/3 = 46 2/3 miles per hour (roughly 47 miles per hour)
Distance = Rate * Time
We are solving for the rate. Susie was driving for a total of 3 hours. The distance she traveled was 100 miles in the first leg, plus 40 miles (40 miles per hour for one hour) in the second leg, or 140 miles total. Use the total distance and total time to solve for the rate.
140/3 = 46 2/3 miles per hour (roughly 47 miles per hour)
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If the average (arithmetic mean) of 
, 
, and 
is twelve, what is the value of 
?
If the average (arithmetic mean) of
The mean will be equal to the sum of the given values, divided by the number of given values.
Use this equation to solve for 
.
Multiply both sides by 3.
Divide both sides by 9.
The mean will be equal to the sum of the given values, divided by the number of given values.
Use this equation to solve for
Multiply both sides by 3.
Divide both sides by 9.
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What is the average number of apples a student has?
What is the average number of apples a student has?
To calculate the average number of apples a student has, the following formula is used.
First, calculate the total number of apples there are. To do this multiply the number of apples by the number of students that have that many apples.
This number divided by the total number of students.
To calculate the average number of apples a student has, the following formula is used.
First, calculate the total number of apples there are. To do this multiply the number of apples by the number of students that have that many apples.
This number divided by the total number of students.
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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?
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?
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.
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.
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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?
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?
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
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
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