Quantitative Aptitude

Statistics

606 Questions
All Ungrouped data dispersion and consistency 209 Unknown terms from given average 124 Grouped data central tendencies 101 Merging means and variances of groups 53 Replacement change in average 27 Alligation and weighted average 21 Data interpretation from tables and charts 20 Net successive percentage change 19 Grouped data variance via step deviation 18 Combination of multiple ratios 1

Statistics Questions

Multiple choice

For a certain dataset, the measurement 15.2 is 2.0 standard deviations below the mean, and the measurement 19.6 is 3.5 standard deviations above the mean. Quantity A The mean of the dataset Quantity B 16.5

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be the mean and S be the standard deviation. 15.2 = M - 2S and 19.6 = M + 3.5S. Subtracting the equations: 4.4 = 5.5S, so S = 0.8. Then M = 15.2 + 2(0.8) = 15.2 + 1.6 = 16.8. Since 16.8 > 16.5, Quantity A is greater.

Multiple choice

The exam scores of 9 students in a class are represented by the set S = {68, 62, 78, 73, 82, 88, 76, 71, 77}. Which of the following options accurately represents the value of the standard deviation for this set of scores?

  1. 2.37

  2. 3.72

  3. 5.78

  4. 7.23

  5. 8.25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mean = (68+62+78+73+82+88+76+71+77)/9 = 675/9 = 75. Variance = [(68-75)^2 + (62-75)^2 + (78-75)^2 + (73-75)^2 + (82-75)^2 + (88-75)^2 + (76-75)^2 + (71-75)^2 + (77-75)^2]/9 = (49+169+9+4+49+169+1+16+4)/9 = 470/9 = 52.22. Standard deviation = sqrt(52.22) = 7.226.

Multiple choice

The numbers of books sold at a certain store over six of the last seven business days were 6, 8, 2, 9, 4, and 7, respectively. If the number of books sold on the seventh day was 3, 6, or 7, for which value is the average number of books sold per day equal to the median number of books sold per day?I. 3 II. 6 III. 7

  1. I only

  2. II only

  3. I and II only

  4. II and III only

  5. I, II, and III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The six known values are 2, 4, 6, 7, 8, and 9, with a sum of 36. If the seventh value is 6, the sorted list is 2, 4, 6, 6, 7, 8, 9, which has a median of 6, and the average is (36 + 6) / 7 = 6. Testing 3 and 7 shows that their averages do not equal their respective medians.

Multiple choice

15, 14, 18, 17, x The mean and the median of the five numbers above are equal. Which of the following is NOT a possible value of x ?

  1. 6

  2. 11

  3. 16

  4. 21
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Numbers: 14, 15, 17, 18, x. Mean = (64+x)/5. Median depends on x. If x is small, median is 15 or 17. If x=6, set is 6, 14, 15, 17, 18. Median=15. Mean=(64+6)/5 = 14. 14 != 15. If x=11, set is 11, 14, 15, 17, 18. Median=15. Mean=(64+11)/5 = 15. 15=15. If x=16, set is 14, 15, 16, 17, 18. Median=16. Mean=(64+16)/5 = 16. 16=16. If x=21, set is 14, 15, 17, 18, 21. Median=17. Mean=(64+21)/5 = 17. 17=17. Only x=6 fails.

Multiple choice

The arithmetic mean score of a group of students in a test was 60. The 15% of the student's mean score is 85 and the 25% of the student's mean score is 30. The mean score of remaining students is

  1. 66.25

  2. 62.25

  3. 58.25

  4. 60.25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total students be N. Mean = 60. Sum = 60N. 15% of students have mean 85 (sum = 0.15N * 85 = 12.75N). 25% have mean 30 (sum = 0.25N * 30 = 7.5N). Remaining 60% have sum = 60N - 12.75N - 7.5N = 39.75N. Mean of remaining = 39.75N / 0.6N = 66.25.

Multiple choice

What is the mean deviation of the first 10 natural numbers?

  1. 2

  2. 2.5

  3. 3

  4. 3.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mean of the first 10 natural numbers is 5.5. The mean deviation is the average of the absolute differences from the mean: (|1-5.5| + |2-5.5| + ... + |10-5.5|) / 10 = (4.5 + 3.5 + 2.5 + 1.5 + 0.5 + 0.5 + 1.5 + 2.5 + 3.5 + 4.5) / 10 = 25 / 10 = 2.5.