Statistics - PSAT Math
Card 1 of 1435
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?
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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?
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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?
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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?
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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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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 ?
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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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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?
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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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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?
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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:
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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?
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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
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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?
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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?
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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?
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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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Find the arithmetic mean of the data set:
13, 21, 25, 37, 51, 52, 58, 83
Find the arithmetic mean of the data set:
13, 21, 25, 37, 51, 52, 58, 83
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13 is the minimum value. 83 is the maximum value. 70 is the range. 44 is the median.
In order to find the arithmetic mean, add the numbers together and divide by the number of numbers.
(13+21+25+37+51+52+58+83)/8 = 340/8 = 42.5
13 is the minimum value. 83 is the maximum value. 70 is the range. 44 is the median.
In order to find the arithmetic mean, add the numbers together and divide by the number of numbers.
(13+21+25+37+51+52+58+83)/8 = 340/8 = 42.5
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Ten students take an exam and score the following grades:
97
86
67
75
89
95
93
75
81
88
What is the mean score on the exam?
Ten students take an exam and score the following grades:
97
86
67
75
89
95
93
75
81
88
What is the mean score on the exam?
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The mean, or average, score is determined by adding up all the scores and then dividing by the total number of tests:
(97+86+67+75+89+95+93+75+81+88) / 10 = 846 / 10 = 84.6
The mean, or average, score is determined by adding up all the scores and then dividing by the total number of tests:
(97+86+67+75+89+95+93+75+81+88) / 10 = 846 / 10 = 84.6
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Choose the statement(s) that holds true for the following set of data:
{50, 63, 54, 59, 67, 61, 54, 68, 58, 66}
I. The median is 60.
II. The mean is 60.
III. There is no mode.
Choose the statement(s) that holds true for the following set of data:
{50, 63, 54, 59, 67, 61, 54, 68, 58, 66}
I. The median is 60.
II. The mean is 60.
III. There is no mode.
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List the numbers in order to find the median: {50, 54, 54, 58, 59, 61, 63, 66, 67, 68}. The middle numbers are 59 and 61 so their average is 60 for the median of the data set making statement I true. Add the list of numbers and divide by 10 to get a mean of 60, making statement II true. There is a mode of 54 so statement III is false.
List the numbers in order to find the median: {50, 54, 54, 58, 59, 61, 63, 66, 67, 68}. The middle numbers are 59 and 61 so their average is 60 for the median of the data set making statement I true. Add the list of numbers and divide by 10 to get a mean of 60, making statement II true. There is a mode of 54 so statement III is false.
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Find the mean in a given set of numbers:
1, 4, 8, 17, 8, 8, 15, 21, 32, 17
Find the mean in a given set of numbers:
1, 4, 8, 17, 8, 8, 15, 21, 32, 17
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In order to find the mean, add all the numbers together (131) and divide by the number of items (10) = 13.1
In order to find the mean, add all the numbers together (131) and divide by the number of items (10) = 13.1
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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}
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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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In a certain game, each of five players received a score between 0 and 100 inclusive. If their average (arithmetic mean) score was 50, what is the greatest possible number of the five players who could have received a score of 75?
In a certain game, each of five players received a score between 0 and 100 inclusive. If their average (arithmetic mean) score was 50, what is the greatest possible number of the five players who could have received a score of 75?
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The question tells us that 50 was the average score of the 5 players, which means that 50 = total points / 5. So, the total points scored in the game must be 5 * 50 = 250.
Going through the answer choices, suppose all five players scored 75—then the total points would be 75 + 75 + 75 + 75 + 75 = 375, which is not 250, so five is not the correct answer.
Suppose four of the five players scored a 75—then the total points for players a, b, c, and d would be 75 + 75 + 75 + 75 = 300, and player e would have to score -50 for the total points to equal 250. Since player e's score cannot equal –50 (the problem says that scores are between 0 and 100), four is not the correct answer.
Now suppose that three of the four players scored a 75—then the total points for players a, b, and c would be 75 + 75 + 75 = 225, meaning d + e would have to equal 25 for the total points to equal 250. This scenario is possible in the game, if, for example, player d scored 12 points and player e scored 13 points. Therefore the greatest possible number of the 5 players who could have scored a 75 is three.
The question tells us that 50 was the average score of the 5 players, which means that 50 = total points / 5. So, the total points scored in the game must be 5 * 50 = 250.
Going through the answer choices, suppose all five players scored 75—then the total points would be 75 + 75 + 75 + 75 + 75 = 375, which is not 250, so five is not the correct answer.
Suppose four of the five players scored a 75—then the total points for players a, b, c, and d would be 75 + 75 + 75 + 75 = 300, and player e would have to score -50 for the total points to equal 250. Since player e's score cannot equal –50 (the problem says that scores are between 0 and 100), four is not the correct answer.
Now suppose that three of the four players scored a 75—then the total points for players a, b, and c would be 75 + 75 + 75 = 225, meaning d + e would have to equal 25 for the total points to equal 250. This scenario is possible in the game, if, for example, player d scored 12 points and player e scored 13 points. Therefore the greatest possible number of the 5 players who could have scored a 75 is three.
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In a certain class, there are are 12 girls and 17 boys. If the average (arithmetic mean) height of the girls is g and the average (arithmetic mean) height of the boys is b, what is the average height of all of the girls and boys in the class?
In a certain class, there are are 12 girls and 17 boys. If the average (arithmetic mean) height of the girls is g and the average (arithmetic mean) height of the boys is b, what is the average height of all of the girls and boys in the class?
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Averages are calculated by the formula: TOTAL SUM FOR THE GROUP/ NUMBER OF ELEMENTS IN THE GROUP. We are told that the average for the 12 girls is g and the average for the 17 boys is b. Our formula for averages tells us that g = TOTAL SUM OF GIRLS’ HEIGHTS / 12 and that b = TOTAL SUM OF BOYS’ HEIGHTS / 17. Rearranging the terms, we see that the TOTAL SUM OF GIRLS’ HEIGHTS = 12_g_ and the TOTAL SUM OF BOYS’ HEIGHTS =17_b_.
Again using our formula for averages, we see that the average height of all of the boys and girls in the class is given by the TOTAL HEIGHT FOR ALL BOYS AND GIRLS / TOTAL NUMBER OF BOYS AND GIRLS. We know the total height for all boys and girls will be the sum of the total girls' height and the total boys' height, or 12_g_ +17_b_, and we know that the total number of boys and girls in the class is 12+17=29. Therefore, the average height for all boys and girls in the class is (12_g_ +17_b_)/29.
Averages are calculated by the formula: TOTAL SUM FOR THE GROUP/ NUMBER OF ELEMENTS IN THE GROUP. We are told that the average for the 12 girls is g and the average for the 17 boys is b. Our formula for averages tells us that g = TOTAL SUM OF GIRLS’ HEIGHTS / 12 and that b = TOTAL SUM OF BOYS’ HEIGHTS / 17. Rearranging the terms, we see that the TOTAL SUM OF GIRLS’ HEIGHTS = 12_g_ and the TOTAL SUM OF BOYS’ HEIGHTS =17_b_.
Again using our formula for averages, we see that the average height of all of the boys and girls in the class is given by the TOTAL HEIGHT FOR ALL BOYS AND GIRLS / TOTAL NUMBER OF BOYS AND GIRLS. We know the total height for all boys and girls will be the sum of the total girls' height and the total boys' height, or 12_g_ +17_b_, and we know that the total number of boys and girls in the class is 12+17=29. Therefore, the average height for all boys and girls in the class is (12_g_ +17_b_)/29.
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