In this post, you will come across all the possible Standard deviation questions that are likely to appear on the GRE.
Questions 1 to 7 are not actual type GRE questions but only test your basic fundamental concepts of standard deviation.
Questions 8 to 35 are actual real-like GRE questions that you will most likely encounter on the GRE test day.
Questions
Question 1
The standard deviation of a set of numbers is a measure of ________.
(A) mean
(B) median
(C) range
(D) dispersion
(E) mode
Question 2
If the standard deviation of a set of numbers is 0, what can be concluded about those numbers?
(A) They are all the same number.
(B) They are all negative numbers.
(C) They are all positive numbers.
(D) They are all fractions
(E) None of the above
Question 3
The standard deviation of a set of numbers increases as the ________ of the numbers increase.
(A) mean
(B) median
(C) mode
(D) range
(E) None of the above
Question 4
If a set of numbers has a small standard deviation, what can be concluded about the numbers in that set?
(A) They are widely dispersed.
(B) They are tightly clustered around the mean.
(C) They are all negative numbers.
(D) The mean of those numbers is small.
(E) None of the above.
Question 5
If a set of numbers has a large standard deviation, what can be concluded about the numbers in that set?
(A) They are tightly clustered around the mean.
(B) They are widely dispersed.
(C) They are all positive numbers.
(D) They are all negative numbers.
(E) None of the above.
Question 6
Which of the following is NOT true about the standard deviation of a set of numbers?
(A) It is a measure of how tightly clustered the numbers are around the mean.
(B) It is never negative.
(C) It is affected by outliers in the data.
(D) It is always equal to the mean.
(E) It is never zero.
Question 7
The standard deviation of a set of numbers can be calculated using which of the following formulas?
(A) (Sum of the numbers) / (Number of numbers)
(B) (Sum of the squares of the numbers) / (Number of numbers)
(C) Square root of ((Sum of the squares of the deviations of the numbers from the mean) / (Number of numbers))
(D) Square root of ((Sum of the numbers) / (Number of numbers))
(E) Square root of ((Sum of the numbers) / (Number of numbers + 1))
Question 8
Given a set of numbers are normally distributed with a mean of 10 and a standard deviation of 2, what percentage of the numbers falls within the range of 6 to 14?
(A) Approximately 68%
(B) Approximately 84%
(C) Approximately 96%
(D) Approximately 99%
(E) None of the above
Question 9
If a set of numbers has a mean of 100 and a standard deviation of 10, what is the standard deviation of the set of numbers that results when each number in the original set is increased by 20?
(A) 10
(B) 12
(C) 20
(D) 30
(E) 200
Question 10
If a set of numbers has a mean of 50 and a standard deviation of 5, what is the standard deviation of the set of numbers that results when each number in the original set is multiplied by 2?
(A) 5
(B) 10
(C) 20
(D) 100
(E) 150
Question 11
If a set of numbers has a mean of 25 and a standard deviation of 5, what is the standard deviation of the set of numbers that results when each number in the original set is divided by 2?
(A) 5
(B) 2.5
(C) 2
(D) 1
(E) 0.5
Question 12
Which of the following sets of numbers will have the largest standard deviation?
(A) 1, 2, 3, 4, 5
(B) 5, 10, 15, 20, 25
(C) -25, -20, -15, -10, -65
(D) 5, 5, 5, 5, 5
(E) 0.1, 0.2, 0.3, 0.4, 0.5
Question 13
If a set of numbers has a mean of 30 and a standard deviation of 5, what is the standard deviation of the set of numbers that results when each number in the original set is increased by 10?
(A) 5
(B) 7
(C) 10
(D) 15
(E) 20
Question 14
A set of numbers has a standard deviation of 4. What is the standard deviation of the set of numbers that results when each number in the original set is multiplied by 2?
(A) 8
(B) 4
(C) 2
(D) 1
(E) 0.5
Question 15
If a set of numbers has a mean of 20 and a standard deviation of 3, what is the standard deviation of the set of numbers that results when each number in the original set is decreased by 5?
(A) 3
(B) 2
(C) 1
(D) 0
(E) -2
Question 16
A list of numbers has a mean of 20 and a standard deviation of 4. If y is a number in the list that is 1.5 standard deviations below the mean, what is the value of y?
Question 17
A random variable X is normally distributed with a mean of 150 and a standard deviation of 8. What is the probability that the value of X is greater than 136?
Question 18
The numbers in data set T have a standard deviation of 6. If a new data set is formed by multiplying each number in T by 2, what is the standard deviation of the numbers in the new data set?
(A) 3
(B) 4
(C) 6
(D) 12
(E) 24
Question 19
The numbers in data set W have a standard deviation of 10. If a new data set is formed by multiplying each number in W by -2, what is the standard deviation of the numbers in the new data set?
Question 20
A group of numbers have a standard deviation of 3. If a new data set is formed by multiplying each number in the set by 5 and then subtracting 7, what is the standard deviation of the numbers in the new data set?
Question 21
A group of numbers have a standard deviation of 8. If a new data set is formed by multiplying each number in the set by -3 and then adding 4, what is the standard deviation of the numbers in the new data set?
Question 22
A group of numbers have a standard deviation of 3. If a new data set is formed by multiplying each number in the set by 0.5 and then adding -4, what is the standard deviation of the numbers in the new data set?
Question 23
A group of numbers have a standard deviation of 7. If a new data set is formed by multiplying each number in the set by 12 and then adding 2 and finally dividing the result by 3, what is the standard deviation of the numbers in the new data set?
Question 24
The numbers in data set U have a standard deviation of 8. If a new data set is formed by subtracting 4 from each number in U, what is the standard deviation of the numbers in the new data set?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Question 25
Each of the following linear equations defines y as a function of x for all integers x from 1 to 1000. For which of the following equations is the standard deviation of the y-values corresponding to all x-values the greatest?
(A) y = 0.5x + 3
(B) y = 2x + 1
(C) y = -x + 5
(D) y = -5x – 4
(E) y = 4x + 2
Question 26
For a certain distribution, the measurement 10.5 is 1.5 standard deviations above the mean, and the measurement 16.0 is 3.0 standard deviations below the mean. What is the mean of the distribution?
(A) 13.3
(B) 13.4
(C) 13.5
(D) 13.6
(E) 13.7
Question 27
The random variable X is normally distributed with a mean of 500, and the value X = 400 is at the 18 percentile of the distribution. Of the following, which is the best estimate of the standard deviation of the distribution?
(A) 50
(B) 75
(C) 95
(D) 100
(E) 110
Question 28
The distribution of the height of students in a certain school has a mean of 160 cm and a standard deviation of 5 cm. Which of the following heights are within 2 standard deviations of the mean of the distribution?
Indicate all such heights.
(A) 145 cm
(B) 148 cm
(C) 155 cm
(D) 165 cm
(E) 169 cm
(F) 180 cm
Question 29
Suppose the standard deviation of the numbers a, b, and c is 2. What is the standard deviation of a+4, b+4, and c+4 ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Question 30
y,-8,-19
If the standard deviation of the three numbers in the list above is 7, what is the standard deviation of y-21, -40, and -29 ?
(A) -14
(B) -7
(C) 0
(D) 7
(E) 84
Question 31
List A consists of 15 numbers whose standard deviation is 5. List B is formed by subtracting 2 from each number in list A.
Quantity A: The standard deviation of the numbers in list B
Quantity B: 5
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Question 32
List P consists of the four different numbers a, b, c, and d. List Q consists of the four numbers -6a-20, -6b-20, -6c-20 , and -6d-20.
Quantity A: The standard deviation of the numbers in list P
Quantity B: The standard deviation of the numbers in list Q
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Question 33
Quantity A: The standard deviation of weights of 10 individuals whose weights range from 150 pounds to 180 pounds, inclusive
Quantity B: The standard deviation of weights of 10 individuals whose weights range from 160 pounds to 170 pounds, inclusive
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Question 34
Which of the following lists has the greatest standard deviation?
(A) -40, -30, -20, -10, 0
(B) -40, -20, -20, -20, 0
(C) -40, -25, -20, -15, 0
(D) -40, -40, -20, 0, 0
(E) -30, -30, -20, -10, -10
Question 35
Quantity A: The standard deviation of the salaries of 8 employees reported as $40,000, $60,000, $70,000, $80,000, $100,000, $120,000, $140,000, $160,000.
Quantity B: The standard deviation of the actual salaries of these 8 employees, with two of the reported salaries being $10,000 greater and $10,000 less than the actual salary.
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.