GRE Math : How to find arithmetic mean
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Example Questions
Example Question #13 : Statistics
A certain function takes the value 1 with probability 1/2, 2 with probability 1/3, and 3 with probability 1/6. What is the mean value of the function?
2
8/9
7/3
5/3
3/2
5/3
To find the mean or expected value, we multiply each value by its corresponding probability and add them up. So the mean = 1(1/2) + 2(1/3) + 3(1/6) = 5/3.
Example Question #11 : How To Find Arithmetic Mean
In the number set {12, 7, 2, 14, 12, 8, 9, 6, 11} f equals the mean, g equals the median, h equals the mode, and j equals the range.
Which statement is true?
h < j = f = g
j = f < g = h
j < g < h = f
f = g < j = h
f < g = h < j
f = g < j = h
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
Example Question #12 : How To Find Arithmetic Mean
In a regular 52-card deck of cards, what is the expected number of aces in a 5-card hand?
5/13
5/12
1/6
1/4
1/13
5/13
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.
Example Question #102 : Data Analysis
Quantitative Comparison
The average of five numbers is 72.
Quantity A: the sum of the five numbers
Quantity B: 350
Quantity A is greater.
The relationship cannot be determined from the information given.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
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.
Example Question #22 : Statistics
A special 4-sided dice has sides numbered 2, 4, 6, and 8. It lands with the 2 face-up with probability 0.1, 4 face-up with probability 0.2, 6 face-up with probability 0.3, and 8 face-up with probability 0.4. What is the expected value of the numbers that land face-up on the dice?
6
2
8
4
5
6
To find the expected value, we multiply the number by its corresponding probability.
expected value = 2(0.1) + 4(0.2) + 6(0.3) + 8(0.4) = 6
Example Question #23 : Statistics
The average score on Betty's seven tests last semester was 85. If her average score on the first six tests was 87, what was her score on the seventh test?
84
70
82
77
73
73
sum for all 7 tests = 85 * 7 = 595
sum for first 6 tests = 87 * 6 = 522
score on 7th test = 595 – 522 = 73
Example Question #24 : Statistics
The average of four numbers is 25. The average of three of these numbers is 20.
Quantity A: The value of the fourth number
Quantity B: 35
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Quantity A is greater.
Quantity A is greater.
Let's assume that the three numbers that average 20 are x, y, and z. That means that the sum of x, y and z has to be 60. The average (in this case 20) is the sum of the numbers divided by the quantity of numbers (in this case 3). Thus the sum of the numbers must equal the average (in this case 20) times the number of numbers (in this case 3). Similarly the sum of x, y, z, and the fourth number have to equal 100. If x + y + z = 60 and x + y + z + 4th number = 100 then 4th number has to be 40 which is greater than Option B at 35.
Example Question #25 : Statistics
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?
150
152
145
147
140
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
Example Question #22 : Statistics
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
The relationship cannot be determined from the information given.
Quantity B is greater.
Quantity A is greater.
The two quantities are equal.
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.
Example Question #28 : Statistics
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?
100
96
90
87
93
100
(87 + 85 + 90 + 73 + x) / 5 = 87
335 + x = 435
x = 100
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