Range & Standard Deviation — Practice Set

Bank code: STA-RSD · Section: Statistics · 30 questions — Easy 5 · Medium 8 · Hard 12 · Extreme 5

Adding shifts (SD unchanged); multiplying scales (SD times |k|). Compare spread by eye - don't compute.

Every question below is live in the question bank under the ID shown — the sheet and the portal are the same questions. Attempt a level with the clock running, then check Part C.

---

Part A — Questions

Quantitative Comparison — the four choices are always the same, so they are not reprinted: (A) Column A is greater · (B) Column B is greater · (C) The two quantities are equal · (D) The relationship cannot be determined from the information given

Level 1 · Easy — 5 questions · ~4 min

warm-up — these must be automatic

Q1 · STA-RSD-003 · MCQ · 50s

Which of the following data sets has a standard deviation of 0?

(A) {1, 2, 3, 4, 5}
(B) {0, 0, 1, 0, 0}
(C) {7, 7, 7, 7, 7}
(D) {-2, 0, 2, 0, -2}
(E) {1, 1, 2, 1, 1}

Q2 · STA-RSD-008 · Numeric Entry · 40s

A data set consists of the values 5, 10, 15, 20, 25, and 30. What is the range of this data set? Enter your answer as a number.

Numeric entry — write the number.

Q3 · STA-RSD-009 · MCQ · 55s

Which of the following statements is true for every data set?

(A) The standard deviation is negative if some of the values are negative.
(B) The standard deviation is 0 whenever the mean is 0.
(C) The standard deviation is greater than or equal to 0.
(D) The standard deviation equals the range divided by 2.
(E) The standard deviation increases when every value is increased by the same amount.

Q4 · STA-RSD-011 · MCQ · 55s

A data set has a range of 30 and a minimum value of 15. The value 60 is then added to the data set. What is the range of the new data set?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 75

Q5 · STA-RSD-012 · QC · 45s

Set M = {1, 5, 9}

Set N = {1, 5, 9, 7}

Column A: Range of Set M Column B: Range of Set N

---

Level 2 · Medium — 8 questions · ~9 min

two or three steps, one planted trap each

Q6 · STA-RSD-022 · MCQ · 90s

Each of the following is a set of five numbers. Which set has the greatest standard deviation?

(A) {0, 30, 30, 30, 60}
(B) {0, 0, 0, 50, 50}
(C) {10, 20, 30, 40, 50}
(D) {25, 25, 25, 25, 55}
(E) {0, 15, 30, 45, 60}

Q7 · STA-RSD-023 · QC · 70s

Data set A = {0, 0, 0, 12}

Data set B = {3, 3, 3, 3}

Column A: Standard deviation of Data set A Column B: Standard deviation of Data set B

Q8 · STA-RSD-026 · QC · 70s

Data set P = {2, 4, 6, 8, 10}

Data set Q = {20, 40, 60, 80, 100}

Column A: Standard deviation of Data set P Column B: (Standard deviation of Data set Q) divided by 10

Q9 · STA-RSD-027 · MCQ · 65s

A data set has a mean of 50 and a variance of 16. Every value in the data set is increased by 5. What are the new mean and the new variance?

(A) Mean = 50, Variance = 16
(B) Mean = 55, Variance = 16
(C) Mean = 55, Variance = 21
(D) Mean = 55, Variance = 400
(E) Mean = 250, Variance = 400

Q10 · STA-RSD-030 · Numeric Entry · 60s

A data set consists of the values 8, 12, 15, 19, 21, and 26. The value 26 is removed from the data set. What is the range of the remaining five values? Enter your answer as a number.

Numeric entry — write the number.

Q11 · STA-RSD-031 · MCQ · 65s

Data set A has a standard deviation of 4. Data set B consists of the values of Data set A, each multiplied by -2. What is the standard deviation of Data set B?

(A) -8
(B) -4
(C) 2
(D) 4
(E) 8

Q12 · STA-RSD-033 · Numeric Entry · 65s

A data set has a standard deviation of 6. Every value in the data set is multiplied by 5 and then increased by 3. What is the standard deviation of the resulting data set? Enter your answer as a number.

Numeric entry — write the number.

Q13 · STA-RSD-051 · MCQ · 75s

Scores on a test are normally distributed with a mean of 72 and a standard deviation of 6. Approximately what percent of the scores are greater than 84?

(A) 2.5%
(B) 5%
(C) 16%
(D) 32%
(E) 47.5%

---

Level 3 · Hard — 12 questions · ~20 min

where 162+ is won or lost

Q14 · STA-RSD-034 · MCQ · 100s

Set A = {x, x + 4, x + 8, x + 12, x + 16}, where x is a real number. What is the standard deviation of Set A?

(A) 4
(B) 8
(C) sqrt(32)
(D) sqrt(40)
(E) The standard deviation depends on the value of x.

Q15 · STA-RSD-035 · QC · 110s

Set G = {1, 2, 3, 4, 5, 6, 7}. Set H consists of the seven values of Set G together with one additional value v, where v is an integer and 1 <= v <= 7.

Column A: Standard deviation of Set H Column B: Standard deviation of Set G

Q16 · STA-RSD-036 · Numeric Entry · 105s

A data set has a mean of 10 and a standard deviation of 3. Every value x in the data set is replaced by ax + b, where a and b are constants and a > 0. The resulting data set has a mean of 57 and a standard deviation of 12. What is the value of b? Enter your answer as a number.

Numeric entry — write the number.

Q17 · STA-RSD-037 · MCQ · 100s

The heights of the adults in a large population are normally distributed with a mean of 170 cm and a standard deviation of 8 cm. Approximately what percent of these adults have heights between 162 cm and 186 cm?

(A) 34%
(B) 47.5%
(C) 68%
(D) 81.5%
(E) 95%

Q18 · STA-RSD-038 · QC · 110s

A data set consists of 6 distinct positive integers whose range is 10.

Column A: The greatest possible standard deviation of the data set Column B: 5

Q19 · STA-RSD-039 · Select all that apply · 110s

Set S = {4, 7, 10, 13, 16}. Which of the following sets have the same standard deviation as Set S? Select all that apply.

(A) {14, 17, 20, 23, 26}
(B) {8, 14, 20, 26, 32}
(C) {16, 13, 10, 7, 4}
(D) {-4, -7, -10, -13, -16}
(E) {4, 7, 10, 13, 16, 10}

Q20 · STA-RSD-040 · MCQ · 100s

The standard deviation of the data set {a, b, c} is 5. What is the standard deviation of the data set {a - 3, b - 3, c - 3, a - 3, b - 3, c - 3}?

(A) 2
(B) 5
(C) 5 x sqrt(2)
(D) 10
(E) Cannot be determined from the information given

Q21 · STA-RSD-041 · Numeric Entry · 90s

Data set A = {2, 4, 6, 8, 10} has a variance of 8. Data set B is formed by replacing each element x of Data set A with 3x + 7. What is the variance of Data set B? Enter your answer as a number.

Numeric entry — write the number.

Q22 · STA-RSD-042 · Select all that apply · 110s

Data set J and Data set K each consist of exactly 4 positive integers. Data set J has range 6 and Data set K has range 10. Which of the following must be true? Select all that apply.

(A) The greatest value in K is greater than the greatest value in J.
(B) The least value in K is less than the least value in J.
(C) The standard deviation of K is greater than the standard deviation of J.
(D) At least one value in K is different from every value in J.
(E) The mean of K could equal the mean of J.

Q23 · STA-RSD-043 · MCQ · 95s

A data set has n values, a mean of m, and a standard deviation of s, where n > 1 and s > 0. One additional value, equal to m, is added to the data set. What happens to the standard deviation?

(A) It increases.
(B) It decreases.
(C) It stays the same.
(D) It becomes 0.
(E) It increases if n is small and decreases if n is large.

Q24 · STA-RSD-044 · Numeric Entry · 100s

Set A = {k, k + 3, k + 6, k + 9, k + 12} and Set B = {m, m + 1, m + 2, m + 3, m + 4}, where k and m are integers. What is the variance of Set A divided by the variance of Set B? Enter your answer as a number.

Numeric entry — write the number.

Q25 · STA-RSD-045 · Select all that apply · 100s

The data set {1, 3, 5, 7, 9} has mean 5, range 8, and variance 8. Which of the following statements about the data set {2, 6, 10, 14, 18} are true? Select all that apply.

(A) The mean is 10.
(B) The range is 8.
(C) The standard deviation is 2 x sqrt(8).
(D) The variance is 16.
(E) The standard deviation is 4 x sqrt(8).

---

Level 4 · Extreme — 5 questions · ~11 min

165+ — expect to need the insight, not the grind

Q26 · STA-RSD-046 · QC · 130s

Set A consists of n integers, where n > 1, and has mean m and standard deviation s, where s > 0. Set B consists of the n integers of Set A together with one additional value equal to m + s.

Column A: Standard deviation of Set B Column B: s

Q27 · STA-RSD-047 · Numeric Entry · 130s

A data set of 4 values has a mean of 10 and a variance of 20. Two of the values are 4 and 8. What is the greatest of the four values? Enter your answer as a number.

Numeric entry — write the number.

Q28 · STA-RSD-048 · Select all that apply · 125s

Data set D has n values, mean m, and standard deviation s, where s > 0. Data set E is formed by replacing every value x of D with (x - m)/s. Which of the following must be true of Data set E? Select all that apply.

(A) The mean of E is 0.
(B) The standard deviation of E is 1.
(C) The range of E equals the range of D divided by s.
(D) The variance of E is s.
(E) Every value of E lies between -1 and 1.

Q29 · STA-RSD-049 · Select all that apply · 130s

Data sets X and Y each consist of 5 positive integers, and their standard deviations are equal: SD(X) = SD(Y) = s. Data set Z consists of all 10 values from X and Y together. Which of the following must be true? Select all that apply.

(A) The mean of Z equals the average of the mean of X and the mean of Y.
(B) The standard deviation of Z equals s.
(C) The range of Z equals the range of X plus the range of Y.
(D) If the mean of X equals the mean of Y, then the standard deviation of Z is at least s.
(E) The range of Z is at least as large as the range of X.

Q30 · STA-RSD-050 · MCQ · 130s

A data set of 10 values has a mean of 50 and a standard deviation of 10. A second data set of 10 values has a mean of 70 and a standard deviation of 10. The two data sets are combined into a single data set of 20 values. What is the standard deviation of the combined data set?

(A) 10
(B) 10 x sqrt(2)
(C) 10 x sqrt(5)
(D) 20
(E) Cannot be determined from the information given

---