Statistics - GRE Quantitative Reasoning
Card 1 of 456
Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
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The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
Tap to reveal answer
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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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?
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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.
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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?
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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
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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
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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.
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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?
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(87 + 85 + 90 + 73 + x) / 5 = 87
335 + x = 435
x = 100
(87 + 85 + 90 + 73 + x) / 5 = 87
335 + x = 435
x = 100
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Lucy averages 83% on her first 5 tests. What must she score on her sixth test to raise her class average to an 84, assuming all tests are weighted equally?
Lucy averages 83% on her first 5 tests. What must she score on her sixth test to raise her class average to an 84, assuming all tests are weighted equally?
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For the first 5 tests, Sum / 5 = 83, so Sum = 5 * 83 = 415.
Now to solve for the last test, (415 + x) / 6 = 84. Then 415 + x = 504, and x = 89.
For the first 5 tests, Sum / 5 = 83, so Sum = 5 * 83 = 415.
Now to solve for the last test, (415 + x) / 6 = 84. Then 415 + x = 504, and x = 89.
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There exists a function f(x) = 3_x_ + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?
There exists a function f(x) = 3_x_ + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?
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First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:
average = (8 + 11 + 14 + 17 + 20) / 5 = 14
First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:
average = (8 + 11 + 14 + 17 + 20) / 5 = 14
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What is the arithmetic mean (average) of the following set of numbers:
34, 26, 18, 12, 40
What is the arithmetic mean (average) of the following set of numbers:
34, 26, 18, 12, 40
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If in a set of numbers, the numbers are: 
, the average is automatically 
.
To find the average, add up the sum of all the numbers and divide by the number of items present.
If in a set of numbers, the numbers are:
To find the average, add up the sum of all the numbers and divide by the number of items present.
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What is the average (arithmetic mean) of all multiples of five from 5 to 45 inclusive?
What is the average (arithmetic mean) of all multiples of five from 5 to 45 inclusive?
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All multiples of 5 must first be added.
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 = 225
Because we added 9 terms, the product must be divided by 9.
225 / 9 = 25.
25 is the average.
All multiples of 5 must first be added.
5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 = 225
Because we added 9 terms, the product must be divided by 9.
225 / 9 = 25.
25 is the average.
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Find the mode of the following set of numbers:
4,6,12,9,12,90,12,18,12,12,12,4,4,4,9,7,76
Find the mode of the following set of numbers:
4,6,12,9,12,90,12,18,12,12,12,4,4,4,9,7,76
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Mode is the item that appears most often.
Mode is the item that appears most often.
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Find the mode:
Find the mode:
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The mode is the number that appears most frequently in a given set.
The mode is the number that appears most frequently in a given set.
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The medians of the following two sets of numbers are equal, and
the sets are arranged in ascending order
{1, 4, x, 8} and {2, 5, y, 9}. What is y – x?
The medians of the following two sets of numbers are equal, and
the sets are arranged in ascending order
{1, 4, x, 8} and {2, 5, y, 9}. What is y – x?
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Answer: –1
Explanation: Recall that the median of an even-numbered set of numbers is the arithmetic mean of the pair of middle terms. Thus (4 + x)/2 = median of the first set and (5 + y)/2 = median of the second set. Since both medians are equal, we can set the equations equal to eachother. (4 + x)/2 = (5 + y)/2. Multiply both sides by 2 and we get 4 + x = 5 + y. We also know that 4 < x < 8 and 5 < y < 9, since the sets are arranged in ascending order. This narrows our options for x and y down significantly. Plugging in various values will eventually get you to x = 7 and y = 6, since 7 + 4 = 11 and 5 + 6 = 11, and thus the median in both cases would be 5.5. Thus, y – x = –1.
Answer: –1
Explanation: Recall that the median of an even-numbered set of numbers is the arithmetic mean of the pair of middle terms. Thus (4 + x)/2 = median of the first set and (5 + y)/2 = median of the second set. Since both medians are equal, we can set the equations equal to eachother. (4 + x)/2 = (5 + y)/2. Multiply both sides by 2 and we get 4 + x = 5 + y. We also know that 4 < x < 8 and 5 < y < 9, since the sets are arranged in ascending order. This narrows our options for x and y down significantly. Plugging in various values will eventually get you to x = 7 and y = 6, since 7 + 4 = 11 and 5 + 6 = 11, and thus the median in both cases would be 5.5. Thus, y – x = –1.
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There are 3,500 people in group A and 5,000 people in group B:
Car Type % in Group A Who Own % in Group B Who Own Motorbike 4 9 Sedan 35 25 Minivan 22 15 Van 9 12 Coupe 3 6
What is the median of the number of people in group B who own either a minivan, van, or coupe?
There are 3,500 people in group A and 5,000 people in group B:
| Car Type | % in Group A Who Own | % in Group B Who Own |
|---|---|---|
| Motorbike | 4 | 9 |
| Sedan | 35 | 25 |
| Minivan | 22 | 15 |
| Van | 9 | 12 |
| Coupe | 3 | 6 |
What is the median of the number of people in group B who own either a minivan, van, or coupe?
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Treat the percentages as a list, as we are including every demographic from the 3 vehicle types mentioned. If we do each 0.06(5000), 0.12(5000), and 0.15(5000) we note from observation that the median, or middle value, would have to be the 12% row since the sample size does not change. The question asks for EITHER of the 3 categories, so we can ignore the other two.
0.12(5000) = 600(van) is the median of the 3 categories.
Treat the percentages as a list, as we are including every demographic from the 3 vehicle types mentioned. If we do each 0.06(5000), 0.12(5000), and 0.15(5000) we note from observation that the median, or middle value, would have to be the 12% row since the sample size does not change. The question asks for EITHER of the 3 categories, so we can ignore the other two.
0.12(5000) = 600(van) is the median of the 3 categories.
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