How to find arithmetic mean - GRE Quantitative Reasoning
Card 1 of 312
Column A
The mean of the sample of numbers 2, 5, and 10.
Column B
The mean of the sample of numbers 1, 5, and 15.
Column A
The mean of the sample of numbers 2, 5, and 10.
Column B
The mean of the sample of numbers 1, 5, and 15.
Tap to reveal answer
The arithmetic mean is the average of the sum of a set of numbers divided by the total number of numbers in the set. This is not to be confused with median or mode.
In Column A, the mean of 5.66 is obtained when the sum (17) is divided by the number of values in the set (3).
In Column B, the mean of 7 is obtained when 21 is divided by 3. Because 7 is greater than 5.66, Column B is greater. The answer is Column B.
The arithmetic mean is the average of the sum of a set of numbers divided by the total number of numbers in the set. This is not to be confused with median or mode.
In Column A, the mean of 5.66 is obtained when the sum (17) is divided by the number of values in the set (3).
In Column B, the mean of 7 is obtained when 21 is divided by 3. Because 7 is greater than 5.66, Column B is greater. The answer is Column B.
← Didn't Know|Knew It →
Bill runs for 30 minutes at 8 mph and then runs for 15 minutes at 13mph. What was his average speed during his entire run?
Bill runs for 30 minutes at 8 mph and then runs for 15 minutes at 13mph. What was his average speed during his entire run?
Tap to reveal answer
Rate = distance/time.
Find the distance for each individual segment of the run (4 miles and 3.25miles). Then add total distance and divide by total time to get the average rate, while making sure the units are compatible (miles per hour not miles per minute), which means the total 45 minute run time needs to be converted to 0.75 of an hour; therefore (4miles + 3.25 miles/0.75 hour) is the final answer.
Rate = distance/time.
Find the distance for each individual segment of the run (4 miles and 3.25miles). Then add total distance and divide by total time to get the average rate, while making sure the units are compatible (miles per hour not miles per minute), which means the total 45 minute run time needs to be converted to 0.75 of an hour; therefore (4miles + 3.25 miles/0.75 hour) is the final answer.
← Didn't Know|Knew It →
Sample Set A has 25 data points with an arithmetic mean of 50.
Sample Set B has 75 data points with an arithmetic mean of 100.
Quantity A: The arithmetic mean of the 100 data points encompassing A and B
Quantity B: 80
Sample Set A has 25 data points with an arithmetic mean of 50.
Sample Set B has 75 data points with an arithmetic mean of 100.
Quantity A: The arithmetic mean of the 100 data points encompassing A and B
Quantity B: 80
Tap to reveal answer
Note that:
The arithmetic mean of the 100 data points encompassing A and B =
(total data of Sample Set A + total data of Sample Set B)/100
We have Mean of Sample Set A = 50, or:
(total of Sample Set A) / 25 = 50
And we have Mean of Sample Set B = 100, or:
(total of Sample Set B) / 75 = 100
We get denominators of 100 by dividing both of the equations:
Divide \[(total of Sample Set A) / 25 = 50\] by 4:
(total of Sample Set A) / 100 = 50/4 = 25/2
Multiply \[(total of Sample Set B)/75 = 100\] by 3/4:
(total of Sample Set B)/100 = 75
Now add the two equations together:
(total data of Sample Set A + total data of Sample Set B)/100
= 75 + 25/2 > 80
Note that:
The arithmetic mean of the 100 data points encompassing A and B =
(total data of Sample Set A + total data of Sample Set B)/100
We have Mean of Sample Set A = 50, or:
(total of Sample Set A) / 25 = 50
And we have Mean of Sample Set B = 100, or:
(total of Sample Set B) / 75 = 100
We get denominators of 100 by dividing both of the equations:
Divide \[(total of Sample Set A) / 25 = 50\] by 4:
(total of Sample Set A) / 100 = 50/4 = 25/2
Multiply \[(total of Sample Set B)/75 = 100\] by 3/4:
(total of Sample Set B)/100 = 75
Now add the two equations together:
(total data of Sample Set A + total data of Sample Set B)/100
= 75 + 25/2 > 80
← Didn't Know|Knew It →
The average (arithmetic mean) of x, y and z is 15. If w is 10, then what is the average of w, x, y and z?
The average (arithmetic mean) of x, y and z is 15. If w is 10, then what is the average of w, x, y and z?
Tap to reveal answer
We can calculate the arithmetic mean by adding up the numbers in a set, and dividing that total by the count of numbers in the set.
Thus, we know that (x + y + z) / 3 = 15. (Multiply both sides by 3.)
x + y + z = 45
We add w = 10 to that, and divide by the new count, 4.
55 / 4 = 13.75
We can calculate the arithmetic mean by adding up the numbers in a set, and dividing that total by the count of numbers in the set.
Thus, we know that (x + y + z) / 3 = 15. (Multiply both sides by 3.)
x + y + z = 45
We add w = 10 to that, and divide by the new count, 4.
55 / 4 = 13.75
← Didn't Know|Knew It →
The combined height of John and Sandy is 130 inches. Sandy, John, and Allen together have a combined height of 215 inches. Sandy and Allen have combined height of 137 inches. How tall is John?
The combined height of John and Sandy is 130 inches. Sandy, John, and Allen together have a combined height of 215 inches. Sandy and Allen have combined height of 137 inches. How tall is John?
Tap to reveal answer
Translate the question into a series of equations:
J + S = 130; J + S + A = 215; S + A = 137
Although there are several ways of approaching this, let us choose the path that is most direct. Given that J, S, A are all involved in the second equation, we can isolate J if we eliminate S and A - which can be done by using the data we have in the third equation. Since S + A = 137, we can rewrite J + S + A = 215 as:
J + 137 = 215.
Now, we only need to solve for J:
J = 215 - 137
J = 78 inches.
Translate the question into a series of equations:
J + S = 130; J + S + A = 215; S + A = 137
Although there are several ways of approaching this, let us choose the path that is most direct. Given that J, S, A are all involved in the second equation, we can isolate J if we eliminate S and A - which can be done by using the data we have in the third equation. Since S + A = 137, we can rewrite J + S + A = 215 as:
J + 137 = 215.
Now, we only need to solve for J:
J = 215 - 137
J = 78 inches.
← Didn't Know|Knew It →
On a given exam, four students have an average score of 81 points. If another student takes the exam, what must he or she score in order to increase the overall average to at least 83 points?
On a given exam, four students have an average score of 81 points. If another student takes the exam, what must he or she score in order to increase the overall average to at least 83 points?
Tap to reveal answer
Begin by translating the current state of affairs into an equation. We know that for four students, the average is ascertained by taking the sum of the scores (s) and dividing that by four:
s / 4 = 81; s = 324
Now, when we add the additional student, that person's score (x) will be added to the value for s. The average of this new group will be divided among five students. We must solve for the case in which the average is 83 points (thus giving us the case for the minimum score x necessary.) This yields the following equation:
(324 + x) / 5 = 83
Solve for x:
324 + x = 415; x = 91
The minimum score necessary is 91 points.
Begin by translating the current state of affairs into an equation. We know that for four students, the average is ascertained by taking the sum of the scores (s) and dividing that by four:
s / 4 = 81; s = 324
Now, when we add the additional student, that person's score (x) will be added to the value for s. The average of this new group will be divided among five students. We must solve for the case in which the average is 83 points (thus giving us the case for the minimum score x necessary.) This yields the following equation:
(324 + x) / 5 = 83
Solve for x:
324 + x = 415; x = 91
The minimum score necessary is 91 points.
← Didn't Know|Knew It →
Find the arithmetic mean of the following series of numbers:
1, 2, 2, 3, 4, 5, 11, 12
Find the arithmetic mean of the following series of numbers:
1, 2, 2, 3, 4, 5, 11, 12
Tap to reveal answer
To find the arithmetic mean of a series of numbers, add up all of the numbers and divide by the number of numbers in the series. Adding all the numbers gives us 40 and there are 8 numbers in the series. 40/8 = 5
To find the arithmetic mean of a series of numbers, add up all of the numbers and divide by the number of numbers in the series. Adding all the numbers gives us 40 and there are 8 numbers in the series. 40/8 = 5
← Didn't Know|Knew It →
Consider the given set of numbers 70, 81, 91, 83, 88, and 55.
A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original?
Consider the given set of numbers 70, 81, 91, 83, 88, and 55.
A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original?
Tap to reveal answer
Reorder the set: 55, 70, 81, 83, 88, 91
Since the set is even, we find the median by taking the average of the middle two values: (81 + 83)/2 = 82
The average of the first set = (55 + 70 + 81 + 83 + 88 + 91)/6 = 468/6 = 78
The new value to be added is 82 * 1.12 = 91.84
This means the new mean is 559.84/7 = 79.9771
The increase in mean value is 79.9771 – 78 = 1.9771
This is (1.9771/78) 100, or 2.535% larger than the original mean.
Reorder the set: 55, 70, 81, 83, 88, 91
Since the set is even, we find the median by taking the average of the middle two values: (81 + 83)/2 = 82
The average of the first set = (55 + 70 + 81 + 83 + 88 + 91)/6 = 468/6 = 78
The new value to be added is 82 * 1.12 = 91.84
This means the new mean is 559.84/7 = 79.9771
The increase in mean value is 79.9771 – 78 = 1.9771
This is (1.9771/78) 100, or 2.535% larger than the original mean.
← Didn't Know|Knew It →
A group of ten candy bars has an average cost of $0.89 per candy bar. How many bars must be bought at the cost of $0.72 a piece to bring the average down to $0.80?
A group of ten candy bars has an average cost of $0.89 per candy bar. How many bars must be bought at the cost of $0.72 a piece to bring the average down to $0.80?
Tap to reveal answer
We know to begin with that for x candy bards:
x / 10 = 0.89; x = 8.90
We are trying to ascertain how many bars (y) must be added to this to amount to have an average of 0.80. This is represented:
(8.9 + 0.72y) / (10 + y) = 0.8
8.9 + 0.72y = 0.8 (10 + y)
8.9 + 0.72y = 8 + 0.8y
8.9 – 8 = 0.8y - 0.72y
0.9 = 0.08y
y = 0.9 / 0.08 = 11.25
However, since we cannot have a partial amount of candy bars, we will have to buy 12.
We know to begin with that for x candy bards:
x / 10 = 0.89; x = 8.90
We are trying to ascertain how many bars (y) must be added to this to amount to have an average of 0.80. This is represented:
(8.9 + 0.72y) / (10 + y) = 0.8
8.9 + 0.72y = 0.8 (10 + y)
8.9 + 0.72y = 8 + 0.8y
8.9 – 8 = 0.8y - 0.72y
0.9 = 0.08y
y = 0.9 / 0.08 = 11.25
However, since we cannot have a partial amount of candy bars, we will have to buy 12.
← Didn't Know|Knew It →
In a given translation project, three translators each took sections of a book to translate. The first translator took 15000 words, which he translated at a rate of 500 words per 20 minutes. The second translator took 200000 words, which he translated at a rate of 1250 words per half hour. The third took 10000 words, which he translated at a rate of 250 words per 15 minutes. In terms of words per hour, what was the overall average translation rate for this project?
In a given translation project, three translators each took sections of a book to translate. The first translator took 15000 words, which he translated at a rate of 500 words per 20 minutes. The second translator took 200000 words, which he translated at a rate of 1250 words per half hour. The third took 10000 words, which he translated at a rate of 250 words per 15 minutes. In terms of words per hour, what was the overall average translation rate for this project?
Tap to reveal answer
To find the answer, we need to know the total words and the total number of hours involved.
The first is easy: 15000 + 200000 + 10000 = 225000 words
To ascertain the number of hours, we have to look at each translator separately. Although there are several ways to do this, let's consider it this way:
Translator 1 can translate at 500 words per 20 minutes OR 1500 words per hour.
Translator 2 can translate at 1250 words per half hour OR 2500 words per hour.
Translator 3 can translate at 250 words per 15 minutes OR 1000 words per hour.
Therefore, we know each translator took the following amount of time:
Translator 1: 15000 / 1500 = 10 hours
Translator 2: 200000 / 2500 = 80 hours
Translator 3: 10000 / 1000 = 10 hours
The total number of hours was therefore 10 + 80 + 10 = 100 hours.
The average rate was 225000 words/100 hours, or 2250 words per hour.
To find the answer, we need to know the total words and the total number of hours involved.
The first is easy: 15000 + 200000 + 10000 = 225000 words
To ascertain the number of hours, we have to look at each translator separately. Although there are several ways to do this, let's consider it this way:
Translator 1 can translate at 500 words per 20 minutes OR 1500 words per hour.
Translator 2 can translate at 1250 words per half hour OR 2500 words per hour.
Translator 3 can translate at 250 words per 15 minutes OR 1000 words per hour.
Therefore, we know each translator took the following amount of time:
Translator 1: 15000 / 1500 = 10 hours
Translator 2: 200000 / 2500 = 80 hours
Translator 3: 10000 / 1000 = 10 hours
The total number of hours was therefore 10 + 80 + 10 = 100 hours.
The average rate was 225000 words/100 hours, or 2250 words per hour.
← Didn't Know|Knew It →
A certain function takes the value 1 with probability 1/2, 2 with probability 1/3, and 3 with probability 1/6. What is the mean value of the function?
A certain function takes the value 1 with probability 1/2, 2 with probability 1/3, and 3 with probability 1/6. What is the mean value of the function?
Tap to reveal answer
To find the mean or expected value, we multiply each value by its corresponding probability and add them up. So the mean = 1(1/2) + 2(1/3) + 3(1/6) = 5/3.
To find the mean or expected value, we multiply each value by its corresponding probability and add them up. So the mean = 1(1/2) + 2(1/3) + 3(1/6) = 5/3.
← Didn't Know|Knew It →
In the number set {12, 7, 2, 14, 12, 8, 9, 6, 11} f equals the mean, g equals the median, h equals the mode, and j equals the range.
Which statement is true?
In the number set {12, 7, 2, 14, 12, 8, 9, 6, 11} f equals the mean, g equals the median, h equals the mode, and j equals the range.
Which statement is true?
Tap to reveal answer
The answer is f = g < j = h.
First rearrange the number set in a convenient form:
{2, 6, 7, 8, 9, 11, 12, 12, 14}
f = 9
g = 9
h = 12
j = 12
The answer is f = g < j = h.
First rearrange the number set in a convenient form:
{2, 6, 7, 8, 9, 11, 12, 12, 14}
f = 9
g = 9
h = 12
j = 12
← Didn't Know|Knew It →
In a regular 52-card deck of cards, what is the expected number of aces in a 5-card hand?
In a regular 52-card deck of cards, what is the expected number of aces in a 5-card hand?
Tap to reveal answer
There are 4 aces in the 52-card deck so the probability of dealing an ace is 4/52 = 1/13. In a 5-card hand, each card is equally likely to be an ace with probability 1/13. So together, the expected number of aces in a 5-card hand is 5 * 1/13 = 5/13.
There are 4 aces in the 52-card deck so the probability of dealing an ace is 4/52 = 1/13. In a 5-card hand, each card is equally likely to be an ace with probability 1/13. So together, the expected number of aces in a 5-card hand is 5 * 1/13 = 5/13.
← Didn't Know|Knew It →
Quantitative Comparison
The average of five numbers is 72.
Quantity A: the sum of the five numbers
Quantity B: 350
Quantitative Comparison
The average of five numbers is 72.
Quantity A: the sum of the five numbers
Quantity B: 350
Tap to reveal answer
We know the formula here is average = sum / number of values. Plugging in the values we have, 72 = sum / 5. Then the sum = 72 * 5 = 360, so Quantity A is greater.
We know the formula here is average = sum / number of values. Plugging in the values we have, 72 = sum / 5. Then the sum = 72 * 5 = 360, so Quantity A is greater.
← Didn't Know|Knew It →
A special 4-sided dice has sides numbered 2, 4, 6, and 8. It lands with the 2 face-up with probability 0.1, 4 face-up with probability 0.2, 6 face-up with probability 0.3, and 8 face-up with probability 0.4. What is the expected value of the numbers that land face-up on the dice?
A special 4-sided dice has sides numbered 2, 4, 6, and 8. It lands with the 2 face-up with probability 0.1, 4 face-up with probability 0.2, 6 face-up with probability 0.3, and 8 face-up with probability 0.4. What is the expected value of the numbers that land face-up on the dice?
Tap to reveal answer
To find the expected value, we multiply the number by its corresponding probability.
expected value = 2(0.1) + 4(0.2) + 6(0.3) + 8(0.4) = 6
To find the expected value, we multiply the number by its corresponding probability.
expected value = 2(0.1) + 4(0.2) + 6(0.3) + 8(0.4) = 6
← Didn't Know|Knew It →
The average score on Betty's seven tests last semester was 85. If her average score on the first six tests was 87, what was her score on the seventh test?
The average score on Betty's seven tests last semester was 85. If her average score on the first six tests was 87, what was her score on the seventh test?
Tap to reveal answer
sum for all 7 tests = 85 * 7 = 595
sum for first 6 tests = 87 * 6 = 522
score on 7th test = 595 – 522 = 73
sum for all 7 tests = 85 * 7 = 595
sum for first 6 tests = 87 * 6 = 522
score on 7th test = 595 – 522 = 73
← Didn't Know|Knew It →
The average of four numbers is 25. The average of three of these numbers is 20.
Quantity A: The value of the fourth number
Quantity B: 35
The average of four numbers is 25. The average of three of these numbers is 20.
Quantity A: The value of the fourth number
Quantity B: 35
Tap to reveal answer
Let's assume that the three numbers that average 20 are x, y, and z. That means that the sum of x, y and z has to be 60. The average (in this case 20) is the sum of the numbers divided by the quantity of numbers (in this case 3). Thus the sum of the numbers must equal the average (in this case 20) times the number of numbers (in this case 3). Similarly the sum of x, y, z, and the fourth number have to equal 100. If x + y + z = 60 and x + y + z + 4th number = 100 then 4th number has to be 40 which is greater than Option B at 35.
Let's assume that the three numbers that average 20 are x, y, and z. That means that the sum of x, y and z has to be 60. The average (in this case 20) is the sum of the numbers divided by the quantity of numbers (in this case 3). Thus the sum of the numbers must equal the average (in this case 20) times the number of numbers (in this case 3). Similarly the sum of x, y, z, and the fourth number have to equal 100. If x + y + z = 60 and x + y + z + 4th number = 100 then 4th number has to be 40 which is greater than Option B at 35.
← Didn't Know|Knew It →
Four groups of college students, consisting of 15, 20, 10, and 18 people respectively, discovered their average group weights to be 162, 148, 153, and 140, respectively. What is the average weight of all the students?
Four groups of college students, consisting of 15, 20, 10, and 18 people respectively, discovered their average group weights to be 162, 148, 153, and 140, respectively. What is the average weight of all the students?
Tap to reveal answer
We know average = sum / number of students. Rearranging this formula gives sum = average * number of students. So to find the total average, we need to add up the four groups' sums and divide by the total number of students.
average = (15 * 162 + 20 * 148 + 10 * 153 + 18 * 140) / (15 + 20 + 10 + 18) = 150
We know average = sum / number of students. Rearranging this formula gives sum = average * number of students. So to find the total average, we need to add up the four groups' sums and divide by the total number of students.
average = (15 * 162 + 20 * 148 + 10 * 153 + 18 * 140) / (15 + 20 + 10 + 18) = 150
← Didn't Know|Knew It →
Quantitative Comparison
The average weight of the 7 cats at the veterinarian's office is 8 pounds. The average weight of the 12 dogs at the vet is 16 pounds.
Quantity A: The average weight of all of the animals
Quantity B: The average weight of the cats plus the average weight of the dogs
Quantitative Comparison
The average weight of the 7 cats at the veterinarian's office is 8 pounds. The average weight of the 12 dogs at the vet is 16 pounds.
Quantity A: The average weight of all of the animals
Quantity B: The average weight of the cats plus the average weight of the dogs
Tap to reveal answer
Quantity B has fewer calculations so let's look at that first. We just need to add up the two averages, so Quantity B = 8 + 16 = 24.
To calculate Quantity A, we need the formula for average = total sum / total number of animals = (7 * 8 + 12 * 16) / (7 + 12) = 248/19 = 13.05.
13.05 is less than 24, so Quantity B is greater.
Quantity B has fewer calculations so let's look at that first. We just need to add up the two averages, so Quantity B = 8 + 16 = 24.
To calculate Quantity A, we need the formula for average = total sum / total number of animals = (7 * 8 + 12 * 16) / (7 + 12) = 248/19 = 13.05.
13.05 is less than 24, so Quantity B is greater.
← Didn't Know|Knew It →
Alice scored an 87, 85, 90, and 73 on her first four tests of the year. If she wants to have an 87% average in the class, what must she score on her 5th test, assuming the five tests are weighted equally?
Alice scored an 87, 85, 90, and 73 on her first four tests of the year. If she wants to have an 87% average in the class, what must she score on her 5th test, assuming the five tests are weighted equally?
Tap to reveal answer
(87 + 85 + 90 + 73 + x) / 5 = 87
335 + x = 435
x = 100
(87 + 85 + 90 + 73 + x) / 5 = 87
335 + x = 435
x = 100
← Didn't Know|Knew It →