How to find arithmetic mean - ACT Math
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In a theatre there are 600 people. Out of this, 100 males have an average age of 50 and 500 females have an average age of 30. To the nearest whole year, what is the average age of the town’s entire population?
In a theatre there are 600 people. Out of this, 100 males have an average age of 50 and 500 females have an average age of 30. To the nearest whole year, what is the average age of the town’s entire population?
To find the average age, compute:
100 * 50 + 500 * 30= 5000+ 15000= 20000. Then divide by the total amount of people that are at the theatre: 20000/600= 33.3=33.
To find the average age, compute:
100 * 50 + 500 * 30= 5000+ 15000= 20000. Then divide by the total amount of people that are at the theatre: 20000/600= 33.3=33.
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LeBron James had played in 7 playoff games. He scored 31, 30, 55, 14, 29, 20, and 12 points in those games. What is his average for those 7 games?
LeBron James had played in 7 playoff games. He scored 31, 30, 55, 14, 29, 20, and 12 points in those games. What is his average for those 7 games?
To find the mean, you have to add all of the items and then divide by the number of items. Finding the sum (31+30+55+14+29+20+12)= 191 and then dividing by 7 would give a result of 27.3. \[Side Note: The Median is 29 and the range is 43.\]
To find the mean, you have to add all of the items and then divide by the number of items. Finding the sum (31+30+55+14+29+20+12)= 191 and then dividing by 7 would give a result of 27.3. \[Side Note: The Median is 29 and the range is 43.\]
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Susan got a job at a store folding the display clothes. If she folds shirts during her whole eight-hour shift, except for her thirty-minute lunch break, Susan can fold 180 shirts. How long does it take her to fold one shirt?
Susan got a job at a store folding the display clothes. If she folds shirts during her whole eight-hour shift, except for her thirty-minute lunch break, Susan can fold 180 shirts. How long does it take her to fold one shirt?
First you convert hours to minutes by multiplying 8 by 60, giving you 480 minutes. You then subtract her 30 minute lunch break, leaving you with 450 minutes. Then divide this by 180 shirts, giving you 2.5 minutes per shirt. Based on the available answer choices, you then multiply by 60 again to get the time in seconds, 150.
First you convert hours to minutes by multiplying 8 by 60, giving you 480 minutes. You then subtract her 30 minute lunch break, leaving you with 450 minutes. Then divide this by 180 shirts, giving you 2.5 minutes per shirt. Based on the available answer choices, you then multiply by 60 again to get the time in seconds, 150.
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Kobe Bryant has averaged about 29.5 points a game through the first 81 games of the NBA season. His goal is to average at least 30 points per game for the season. What is the least amount of points he needs to score in his last game of the season to achieve his goal? (There are 82 games in a season.)
Kobe Bryant has averaged about 29.5 points a game through the first 81 games of the NBA season. His goal is to average at least 30 points per game for the season. What is the least amount of points he needs to score in his last game of the season to achieve his goal? (There are 82 games in a season.)
To find your answer, you would have to set it up like a weighted average because we don’t know what he scored for the 81 games, but we can approximate how many actual points he scored by multiplying 29.5 times 81. Thus, we would get the equation (29.5(81)+x)/82=30. Multiply both sides by 82 to get 2389.5+x=2460. Thus x=70.5 and we would round up to get 71 points.
To find your answer, you would have to set it up like a weighted average because we don’t know what he scored for the 81 games, but we can approximate how many actual points he scored by multiplying 29.5 times 81. Thus, we would get the equation (29.5(81)+x)/82=30. Multiply both sides by 82 to get 2389.5+x=2460. Thus x=70.5 and we would round up to get 71 points.
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Peter received the following 4 grades on math tests: 86, 90, 88, and 96. What was Peter's average score for the 4 tests?
Peter received the following 4 grades on math tests: 86, 90, 88, and 96. What was Peter's average score for the 4 tests?
In order to calculate the average, or arithmetic mean, of numbers in a set, we add up all of the numbers, then divide that total sum by the n (the count of numbers in the set).
Here we have 86, 90, 88, and 96. This gives us n = 4.
We add up 86 + 90 + 88 + 96 = 360. 360 / 4 = 90.
In order to calculate the average, or arithmetic mean, of numbers in a set, we add up all of the numbers, then divide that total sum by the n (the count of numbers in the set).
Here we have 86, 90, 88, and 96. This gives us n = 4.
We add up 86 + 90 + 88 + 96 = 360. 360 / 4 = 90.
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Jack earned $10 on Tuesday. On each following day, through Satuday, he earned $3 more than the preceding day. What were his mean earnings for the five-day period, Tuesday through Saturday?
Jack earned $10 on Tuesday. On each following day, through Satuday, he earned $3 more than the preceding day. What were his mean earnings for the five-day period, Tuesday through Saturday?
Jack earned $10 on Tuesday, $13 on Wednesday, $16 on Thursday, $19 on Friday, and $22 on Saturday. This is a total of $80. Divide that by the total number of days, 5, and the mean is $16.
Jack earned $10 on Tuesday, $13 on Wednesday, $16 on Thursday, $19 on Friday, and $22 on Saturday. This is a total of $80. Divide that by the total number of days, 5, and the mean is $16.
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Ashley scored 80, 80, 83, 85, 90, and 77 on her tests this semester. If she wants an average of 85 on all her tests, which would she have to score on her final test?
Ashley scored 80, 80, 83, 85, 90, and 77 on her tests this semester. If she wants an average of 85 on all her tests, which would she have to score on her final test?
One can set up an equation for the average test score. 85=(80+80+83+85+90+77+x)/7.
Solving for x gives 100.
One can set up an equation for the average test score. 85=(80+80+83+85+90+77+x)/7.
Solving for x gives 100.
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An olympic athlete has just completed a four mile run. His average time was 6 minutes per mile. If he ran the first and last mile in 5 minutes, and the other 2 were the same time as each other, what was the average time for the 2 miles in the middle?
An olympic athlete has just completed a four mile run. His average time was 6 minutes per mile. If he ran the first and last mile in 5 minutes, and the other 2 were the same time as each other, what was the average time for the 2 miles in the middle?
The total time spent by the athlete was 24 minutes, if two of the miles took 10 minutes, then the other two took 14.
14/2 yields an average of 7 miles per minute
The total time spent by the athlete was 24 minutes, if two of the miles took 10 minutes, then the other two took 14.
14/2 yields an average of 7 miles per minute
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Fred has had three algebra tests so far and has one left before he gets a final grade. He wants an "A" in the class, and so he needs at least a 90% average test grade to get an "A". His previous test scores have been 96%, 86%, and 94%. What is the lowest score he can get on his fourth test to get an "A" in the class?
Fred has had three algebra tests so far and has one left before he gets a final grade. He wants an "A" in the class, and so he needs at least a 90% average test grade to get an "A". His previous test scores have been 96%, 86%, and 94%. What is the lowest score he can get on his fourth test to get an "A" in the class?
The following equation can be set up in order to solve for the score on the fourth test, x. The left side of the equation is the average of all of his tests. This is then set equal to 90%, the average test score which guarantees him an A: (96+86+94+x) / 4 = 90. Solving for x, we get x = 84%.
The following equation can be set up in order to solve for the score on the fourth test, x. The left side of the equation is the average of all of his tests. This is then set equal to 90%, the average test score which guarantees him an A: (96+86+94+x) / 4 = 90. Solving for x, we get x = 84%.
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A student has scored 93, 87, and 94 on three of his four exams. In order to maintain a 90 average or above in the class, what is the lowest this student may score on the fourth exam?
A student has scored 93, 87, and 94 on three of his four exams. In order to maintain a 90 average or above in the class, what is the lowest this student may score on the fourth exam?
In order to have an average of 90 over four exams, that means the sum of all the students scores must total to at least 360.
So far, the student has a total sum of 274 points.
360 - 274 yields 86, the minimum score needed to maintain an average of 90 or higher
In order to have an average of 90 over four exams, that means the sum of all the students scores must total to at least 360.
So far, the student has a total sum of 274 points.
360 - 274 yields 86, the minimum score needed to maintain an average of 90 or higher
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Jill has received $200 on her birthday each year for four consecutive years. For the next two years she received $700 in total. For this 6-year period, what was her average yearly amount of birthday money she received?
Jill has received $200 on her birthday each year for four consecutive years. For the next two years she received $700 in total. For this 6-year period, what was her average yearly amount of birthday money she received?
We add $200 times the four years, giving us $800. We then add $700 for the following two years, giving a total of $1,500. We divide this by 6 years, giving us an average of $250 per year.
We add $200 times the four years, giving us $800. We then add $700 for the following two years, giving a total of $1,500. We divide this by 6 years, giving us an average of $250 per year.
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Janice, Candice, Sharon, and Helen have an average height of 65 inches. Janice is the shortest at 55 inches, and Helen is the tallest at 70 inches. What is the average height of Candice and Sharon?
Janice, Candice, Sharon, and Helen have an average height of 65 inches. Janice is the shortest at 55 inches, and Helen is the tallest at 70 inches. What is the average height of Candice and Sharon?
First we find the average height for Janice and Helen, (55 + 70)/2 = 62.5. The average of the height for Candice and Sharon must complement this to achieve the overall average of 65. We can solve for their average by doing (62.5 + x)/2 = 65.
Solving this equation yields an average height of 67.5 inches.
First we find the average height for Janice and Helen, (55 + 70)/2 = 62.5. The average of the height for Candice and Sharon must complement this to achieve the overall average of 65. We can solve for their average by doing (62.5 + x)/2 = 65.
Solving this equation yields an average height of 67.5 inches.
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The mean of five numbers is 40. The mean of the smallest two numbers is 25. What is the mean of the other three numbers?
The mean of five numbers is 40. The mean of the smallest two numbers is 25. What is the mean of the other three numbers?
The equation for the mean of a group of numbers is to find the sum of all of the numbers and then divide by how many numbers are in the group. This means that if we know the mean and how many numbers are in the group, we can find the sum of those numbers.
(sum of all five numbers) / 5 = 40 --> sum of all five numbers = 200
(sum of two smallest numbers) / 2 = 25 --> sum of two smallest numbers = 50
Subtracting the sum of the two smallest numbers from the sum of all five gives us the sum of the remaining three. We can then divide by three to find the mean of those three remaining numbers.
200 – 50 = 150
150 / 3 = 50
The equation for the mean of a group of numbers is to find the sum of all of the numbers and then divide by how many numbers are in the group. This means that if we know the mean and how many numbers are in the group, we can find the sum of those numbers.
(sum of all five numbers) / 5 = 40 --> sum of all five numbers = 200
(sum of two smallest numbers) / 2 = 25 --> sum of two smallest numbers = 50
Subtracting the sum of the two smallest numbers from the sum of all five gives us the sum of the remaining three. We can then divide by three to find the mean of those three remaining numbers.
200 – 50 = 150
150 / 3 = 50
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Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?
Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?
Since a given player’s scoring average can be determined by dividing the sum total of points scored by the number of games, we can determine the total points of the scoring leader by multiplying the average points per game by the total number of games. 18 x 7 = 126. Angela would have to score 1 more point than the current scoring leader. Angela’s current total is 87 points; therefore, she must score 40 (87 + 40 = 127) over the course of the final two games to have the highest average points per game in the league.
Since a given player’s scoring average can be determined by dividing the sum total of points scored by the number of games, we can determine the total points of the scoring leader by multiplying the average points per game by the total number of games. 18 x 7 = 126. Angela would have to score 1 more point than the current scoring leader. Angela’s current total is 87 points; therefore, she must score 40 (87 + 40 = 127) over the course of the final two games to have the highest average points per game in the league.
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What is the mean of the following set of numbers: 13, 15, 100, 54, 345, rounded to the nearest 1’s place?
What is the mean of the following set of numbers: 13, 15, 100, 54, 345, rounded to the nearest 1’s place?
mean = sum of all values divided by the number of values.
mean = sum of all values divided by the number of values.
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A thermometer reads an average of 47.5 °F on a Sunday, rises 2.9 degrees on Monday, and drops 1.7 degrees on Tuesday. What is the average reading of the thermometer on Tuesday?
A thermometer reads an average of 47.5 °F on a Sunday, rises 2.9 degrees on Monday, and drops 1.7 degrees on Tuesday. What is the average reading of the thermometer on Tuesday?
Use 47.5 as a baseline value to add and subtract the subsequent drops on Monday and Tuesday. Thus, 47.5 + 2.9 = 50.4 (Monday); 50.4 - 1.7 = 48.7 (Tuesday).
Use 47.5 as a baseline value to add and subtract the subsequent drops on Monday and Tuesday. Thus, 47.5 + 2.9 = 50.4 (Monday); 50.4 - 1.7 = 48.7 (Tuesday).
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On the chart above, what was the class average for Exam 2? Round to 1 decimal point.
On the chart above, what was the class average for Exam 2? Round to 1 decimal point.
Average = (Sum of Grades) / (# of Grades)
= (85+93+65+70+90+72+65+86+93) / 9
= 719 / 9 = 79.9
Average = (Sum of Grades) / (# of Grades)
= (85+93+65+70+90+72+65+86+93) / 9
= 719 / 9 = 79.9
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Jenny just got her spring report card. She earned 3 As, 2 Bs and one C. If the values assigned to grades are 4 points for an A, 3 points for a B, and 2 points for a C, what is her GPA, rounded to the nearest tenth?
Jenny just got her spring report card. She earned 3 As, 2 Bs and one C. If the values assigned to grades are 4 points for an A, 3 points for a B, and 2 points for a C, what is her GPA, rounded to the nearest tenth?
GPA is the average of the grade points.
GPA = (3*4 + 2*3 + 1*2) / 6 = 3.33
GPA is the average of the grade points.
GPA = (3*4 + 2*3 + 1*2) / 6 = 3.33
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Mark has a job mowing lawns for some of the people in his neighborhood. If Mark gets paid $30 per lawn, and it takes him 40 minutes to mow a lawn, what is his average hourly pay if he typically spends 4 hours total mowing lawns?
Mark has a job mowing lawns for some of the people in his neighborhood. If Mark gets paid $30 per lawn, and it takes him 40 minutes to mow a lawn, what is his average hourly pay if he typically spends 4 hours total mowing lawns?
This question requires us to do a few things. First, we must figure out how many lawns Mark mows in 4 hours.
4 hours x 60 minutes/hr = 240 minutes.
240 minutes ÷ 40 minutes/lawn = 6 lawns.
6 lawns x $30/lawn = $180
So, he made $180 in a matter of 4 hours.
$180 ÷ 4 hours = $45/hr
This question requires us to do a few things. First, we must figure out how many lawns Mark mows in 4 hours.
4 hours x 60 minutes/hr = 240 minutes.
240 minutes ÷ 40 minutes/lawn = 6 lawns.
6 lawns x $30/lawn = $180
So, he made $180 in a matter of 4 hours.
$180 ÷ 4 hours = $45/hr
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Anthony makes $4,000 a month as a bartender 10 months of the year, and for 2 months, he works in a jazz club where he makes $6,000 a month.
What is Anthony's average monthly salary in a year?
Anthony makes $4,000 a month as a bartender 10 months of the year, and for 2 months, he works in a jazz club where he makes $6,000 a month.
What is Anthony's average monthly salary in a year?
In a year, Anthony makes $4,000 x 10 = $40,000
and an additional $6,000 x 2 = $12,000
totaling $52,000
The average monthly salary would be 52,000 ÷ 12 = 4,333
In a year, Anthony makes $4,000 x 10 = $40,000
and an additional $6,000 x 2 = $12,000
totaling $52,000
The average monthly salary would be 52,000 ÷ 12 = 4,333
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