Statistics
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GRE Quantitative Reasoning › Statistics
Column A: The median of the set
Column B: The mean of the set
Column A is greater.
Column B is greater.
Columns A and B are equal.
Cannot be determined.
Explanation
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
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)?
Explanation
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.
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
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Explanation
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
Looking at all the multiples of 5 from 5 to 50, what is the mean of all of those values?
Explanation
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
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
c < b < d < a
b < d < c < a
c < a < d < b
a < b < d < c
d < c < a < b
Explanation
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
Looking at all the multiples of 5 from 5 to 50, what is the mean of all of those values?
Explanation
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
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
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Explanation
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
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: 8, 3, 11, 12, 3, 4, 6, 15, 1 ?
Explanation
The answer is 
First organize the number set 1, 3, 3, 4, 6, 8, 11, 12, 15
a = range = 14
b = mean = 7
c = median = 6
d = mode = 3
so the order is mode<median<mean<range
or d < c < b < a.
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)?
Explanation
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.
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: 8, 3, 11, 12, 3, 4, 6, 15, 1 ?
Explanation
The answer is
First organize the number set 1, 3, 3, 4, 6, 8, 11, 12, 15
a = range = 14
b = mean = 7
c = median = 6
d = mode = 3
so the order is mode<median<mean<range
or d < c < b < a.