Statistics - GRE Quantitative Reasoning

Mode is the item that appears most often.

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.

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 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

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

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.

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

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 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.

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.

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.

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.

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