GRE Math : Data Analysis
Study concepts, example questions & explanations for GRE Math
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Example Questions
Example Question #32 : Statistics
Which statement is true assuming that a represents the range, b represents the mean, c represents the median, and d represents the mode.
Which sequence is correct for the number set: 51, 8, 51, 17, 102, 31, 20
a < b < d < c
c < b < d < a
c < a < d < b
b < d < c < a
d < c < a < b
c < b < d < a
The answer is c < b < d < a.
When we arrange the number set we see: 8, 17, 20, 31, 51, 51, 102
a = range = 94
b = mean = 40
c = median = 31
d = mode = 51
median < mean < mode < range so c < b < d < a
Example Question #33 : Statistics
Jim got scores of 84, 78, 92, and 89 on the first four exams in his math class. What must he get on the fifth exam to have an average score of 88 for all five exams?
93
97
95
91
99
97
Write out the average formula, with x representing the fifth score, and filling in 88 as the average score we want.
Then isolate and solve for x.
Example Question #37 : Statistics
If the average of 
40
70
90
150
80
80
If the average of 
Likewise, if the average of b and c is 110, then their sum must be 220.
Example Question #32 : Arithmetic Mean
The average of 10 test scores is 120 and the average of 30 additional scores is 100.
Quantity A: The weighted average of these scores
Quantity B: 105
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A is greater
Quantity B is greater
The two quantities are equal
The sum of the first ten scores is 1,200 and the sum of the next 30 scores is 3,000. To take the weighted average of all scores, divide the sum of all scores (4,200) by the total number of scores (40), which would equal 105.
Example Question #41 : Statistics
A plane flies from San Francisco to New York City at 600 miles per hour and returns along the same route at 400 miles per hour. What is the average flying speed for the entire route (in miles per hour)?
First, pick a distance, preferably one that is divisible by 400 and 600. As an example, we will use 1,200. If the distance is 1,200, then it took 2 hours to get to New York City and 3 hours to get back to San Francisco. So, the plane traveled 2,400 miles in 5 hours. The average speed is simply 2,400 miles divided by 5 hours, which is 480 miles per hour.
Example Question #42 : Statistics
Column A: The median of the set
Column B: The mean of the set
Column A is greater.
Column B is greater.
Cannot be determined.
Columns A and B are equal.
Column B is greater.
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
Example Question #2 : How To Find Excluded Values
If the average (arithmetic mean) of 
There is not enough information to determine the answer.
If we can find the sum of 
Write out the average formula for the original three quantities. Remember, adding together and dividing by the number of quantities gives the average:
Isolate 
Write out the average formula for the new three quantities:
Combine the integers in the numerator:
Replace 
Example Question #43 : Statistics
The arithmetic mean of a, b, and c is
Quantity A: The arithmetic mean of
Quantity B:
The relationship cannot be established.
Quantity A is greater.
The two quantities are equal.
Quantity B is greater.
The two quantities are equal.
To solve this problem, calculate Quantity A.
The arithmetic mean for a set of values is the sum of these values divided by the total number of values:
For the set 
Now recall that we're told that arithmetic mean of a, b, and c is 
Using this fact, return to what we've written for Quantity A:
Quantity B is also
So the two quantities are equal.
Example Question #44 : Statistics
The arithmetic mean of a and b is
Quantity A:
Quantity B:
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be established.
Quantity A is greater.
The key to this problem is to recognize that Quantity A can be rewritten.
The function
can be written as
Now, recall what we're told about the mean of a and b, namely that it equals 
This is equivalent to saying
From this, we can see that
Therefore, we can find a value for Quantity A:
Quantity A is greater.
Example Question #45 : Statistics
Looking at all the multiples of 5 from 5 to 50, what is the mean of all of those values?
All of the multiples of 5 from 5 to 50 are
The total of all of them is 275.
Then the mean will be 27.5
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