Statistics - GRE Quantitative Reasoning

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.

To find the median, arrange the numbers from smallest to largest:

4,4,4,4,6,7,9,9,12,12,12,12,12,12,18,76,90

There are 17 numbers in total. Since 17 is an odd number, the median will be the middle number of the set. In this case, it is the 9th number, which is 12.

16, 19, 16, 7, 2, 20, 9, 5

Order the numbers from smallest to largest.

2,5,7,9,16,16,19,20

The median is the number in the middle.

In this case, there is a 9 and 16 in the middle.

When that happens, take the average of the two numbers.

Begin by ordering the set from smallest to largest:

Already, we see that the mode is 8. Find the median by taking the average of the two middle numbers:

Find the mean by adding all numbers and dividing by the total number of terms:

Of the three, the mean of the set is the largest.

To solve this problem, we must be aware of the definition of a median for a set of numbers. The median is defined as the number that is in middle of a set of numbers sorted from smallest to largest. Therefore we must first sort the numbers from largest to smallest.

34,43,45,50,56,65,70,76,76,82,87,88,92,95,100

43,45,50,56,65,70,76,76,81,87,88,82,95

45,50,56,65,70,76,76,81,87,88,82

50,56,65,70,76,76,81,87,88

56,65,70,76,76,81,87

65,70,76,76,81

70,76,76

76

Then by slowly eliminating the smallest and the largest numbers we find that the median score for this test is 76.

is an unknown value, but it can be found given what we know about the mean of the set :

Now, is out of order; arrange in numerically:

Since there are even number of values, the median is the mean of the two middle most values:

Begin by reordering the set in numerical order:

Then becomes

Since there is an odd number of values, the median is the middle value.

Quantity B:

Now, to find the arithmetic mean, take the sum of values divided by the total number of values.

Quantity A:

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.

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.

To find the median, arrange the numbers from smallest to largest:

4,4,4,4,6,7,9,9,12,12,12,12,12,12,18,76,90

There are 17 numbers in total. Since 17 is an odd number, the median will be the middle number of the set. In this case, it is the 9th number, which is 12.

16, 19, 16, 7, 2, 20, 9, 5

Order the numbers from smallest to largest.

2,5,7,9,16,16,19,20

The median is the number in the middle.

In this case, there is a 9 and 16 in the middle.

When that happens, take the average of the two numbers.

Begin by ordering the set from smallest to largest:

Already, we see that the mode is 8. Find the median by taking the average of the two middle numbers:

Find the mean by adding all numbers and dividing by the total number of terms:

Of the three, the mean of the set is the largest.

To solve this problem, we must be aware of the definition of a median for a set of numbers. The median is defined as the number that is in middle of a set of numbers sorted from smallest to largest. Therefore we must first sort the numbers from largest to smallest.

34,43,45,50,56,65,70,76,76,82,87,88,92,95,100

43,45,50,56,65,70,76,76,81,87,88,82,95

45,50,56,65,70,76,76,81,87,88,82

50,56,65,70,76,76,81,87,88

56,65,70,76,76,81,87

65,70,76,76,81

70,76,76

76

Then by slowly eliminating the smallest and the largest numbers we find that the median score for this test is 76.

is an unknown value, but it can be found given what we know about the mean of the set :

Now, is out of order; arrange in numerically:

Since there are even number of values, the median is the mean of the two middle most values:

Begin by reordering the set in numerical order:

Then becomes

Since there is an odd number of values, the median is the middle value.

Quantity B:

Now, to find the arithmetic mean, take the sum of values divided by the total number of values.

Quantity A:

The average is the sum of the points scored in the last nine games divided by 9, which equals 86. The mode is the score which occurs most often, 82. 86 – 82 = 4

Mode is the item that appears most often.

The mode is the number that appears most frequently in a given set.

To solve this problem, we must be clear on the definition of the mode of a set of numbers. The mode is defined as the number that occurs the most frequently within a set of numbers. In this case, we can see that the number 1 occurs 3 times, the number 2 occurs 4 times, the number 3 occurs 3 times, the number 4 occurs 2 times and the number 5 occurs only one time. Therefore the mode of this survey is 2.