Statistics and Averages — GMAT Focus Questions

22 GMAT Focus practice questions on Statistics and Averages, part of Quantitative Reasoning. Below are 12 of them in full, each with the answer and a written explanation.

Questions & explanations

1. Set A consists of the numbers {2, 5, x, 9, 11, y}, where x and y are positive integers. If the median of the set is 7, and x < y, what is the value of x?

  1. 3
  2. 5
  3. 6
  4. 7
  5. 8

Answer: 5

Sorted order: 2,5,x,9,11,y (since x<y and x<9, y>11? y could be >11 or between 9 and 11). With 6 numbers, median is average of 3rd and 4th. For median 7, (x+9)/2=7 → x+9=14 → x=5. Then y must be >9? if x=5, sorted: 2,5,5,9,11,y. Median = (5+9)/2=7. y can be any >9, condition x<y holds.

2. Which of the following best describes the standard deviation of a set of numbers?

  1. The average of the numbers in the set
  2. The difference between the largest and smallest numbers
  3. A measure of how spread out the numbers are from the mean
  4. The middle value when the numbers are arranged in order
  5. The number that appears most frequently

Answer: A measure of how spread out the numbers are from the mean

Standard deviation quantifies the dispersion of data points around the mean. A small standard deviation indicates data points are close to the mean, while a large one indicates they are spread out. Option c correctly defines it as a measure of spread from the mean.

3. Data set A: {10, 20, 30, 40, 50}. Data set B: {15, 20, 25, 30, 35}. Which of the following is true about the standard deviations of the two sets?

  1. Standard deviation of A is greater than that of B.
  2. Standard deviation of B is greater than that of A.
  3. The standard deviations are equal.
  4. Standard deviation of A is twice that of B.
  5. Cannot be determined from the information given.

Answer: Standard deviation of A is greater than that of B.

Set A has values spread from 10 to 50 (range 40), while set B is from 15 to 35 (range 20). Since the values in A are more spread out from the mean (30), its standard deviation is larger. No calculation needed; visual spread indicates greater SD.

4. The following data set shows the number of books read by students in a month: 2, 3, 3, 5, 5, 5, 7, 7, 8, 8, 8, 9. What is the mode of the data set?

  1. 5 only
  2. 8 only
  3. 5 and 8
  4. 3, 5, and 8
  5. No mode

Answer: 5 and 8

Count frequencies: 2 appears once, 3 appears twice, 5 appears three times, 7 appears twice, 8 appears three times, 9 appears once. The highest frequency is 3, occurring for both 5 and 8. Thus the data set is multimodal with modes 5 and 8.

5. Data set A: {10, 10, 10, 10, 10}. Data set B: {5, 5, 10, 15, 15}. Which statement is true?

  1. Set A has a larger standard deviation than set B.
  2. Set B has a larger standard deviation than set A.
  3. Both sets have the same standard deviation.
  4. Set A has a standard deviation of 10.
  5. Set B has a standard deviation of 0.

Answer: Set B has a larger standard deviation than set A.

Set A has all values equal to the mean (10), so standard deviation is 0. Set B has values spread from 5 to 15, so its standard deviation is greater than 0. Thus, set B has a larger standard deviation.

6. Data set S consists of the numbers {2, 2, 2, 5, 5, 5, 5, 5, 5, 5}. Which of the following is true about the standard deviation of S?

  1. It is 0 because there are repeated values.
  2. It is less than the standard deviation of {2, 5}.
  3. It is greater than the standard deviation of {2, 5}.
  4. It is equal to the standard deviation of {2, 5}.
  5. It cannot be determined without knowing the exact values.

Answer: It is less than the standard deviation of {2, 5}.

Standard deviation measures spread. Set S has many 5's and few 2's, so the mean is closer to 5, reducing spread compared to {2,5} which has equal frequency and mean 3.5. Thus SD of S is smaller.

7. A data set consists of the following numbers: 3, 7, 9, 12, 15, 18, 21. If the number 10 is added to the set, what is the median of the new set?

  1. 10
  2. 11
  3. 12
  4. 13
  5. 14

Answer: 11

Original set (odd count 7): sorted 3,7,9,12,15,18,21; median = 12. Adding 10 gives 8 numbers (even). New sorted: 3,7,9,10,12,15,18,21. Median = average of 4th and 5th = (10+12)/2 = 11.

8. A store sells two types of coffee: Type A at $12 per pound and Type B at $18 per pound. How many pounds of Type A must be mixed with 10 pounds of Type B to create a blend that costs $15 per pound?

  1. 5
  2. 10
  3. 12
  4. 15
  5. 20

Answer: 10

Let x = pounds of Type A. Total cost = 12x + 18(10) = 12x + 180. Total weight = x + 10. Average cost = (12x + 180)/(x + 10) = 15. Multiply: 12x + 180 = 15x + 150 → 30 = 3x → x = 10.

9. A company has two departments: Sales and Marketing. The Sales department has 40 employees with an average salary of $50,000. The Marketing department has 60 employees with an average salary of $70,000. What is the weighted average salary of all employees in the company, using the percentages of employees as weights?

  1. $58,000
  2. $60,000
  3. $62,000
  4. $64,000
  5. $66,000

Answer: $62,000

Total employees = 40+60 = 100. Sales weight = 40/100 = 0.4, Marketing weight = 60/100 = 0.6. Weighted average = (0.4 × 50,000) + (0.6 × 70,000) = 20,000 + 42,000 = $62,000.

10. A company has three departments: A with 10 employees averaging $50,000 salary, B with 20 employees averaging $60,000, and C with 30 employees averaging $70,000. What is the average salary across all departments?

  1. $60,000
  2. $62,500
  3. $63,333
  4. $65,000
  5. $66,667

Answer: $63,333

Total salary = 10×50000 + 20×60000 + 30×70000 = 500000 + 1200000 + 2100000 = 3,800,000. Total employees = 10+20+30 = 60. Average = 3,800,000 / 60 = 63,333.33 ≈ $63,333.

11. Class A has 20 students with an average score of 80. Class B has 30 students with an average score of 70. What is the overall average score for the two classes combined?

  1. 73
  2. 74
  3. 75
  4. 76
  5. 77

Answer: 74

Total points for class A = 20 × 80 = 1600. Total points for class B = 30 × 70 = 2100. Combined total = 3700. Combined students = 50. Overall average = 3700 / 50 = 74.

12. The standard deviation of a set of numbers is 5. If 10 is added to each number in the set, what is the new standard deviation?

  1. 5
  2. 10
  3. 15
  4. 50
  5. Cannot be determined

Answer: 5

Adding a constant to every value shifts the entire distribution but does not change the spread. Standard deviation measures dispersion, so it remains unchanged at 5.

More Quantitative Reasoning topics

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