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

The mean of 100 observations is 24. On adding 6 to each observation and then multiplied with 2.5, what will be the new average of those observations?

  1. 30

  2. 75

  3. 35

  4. 60

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original mean is 24 for 100 observations, so total is 2400. Adding 6 to each observation adds 600 to the total (6 x 100), making it 3000. Multiplying by 2.5 gives 7500. The new mean is 7500/100 = 75. Alternatively: new mean = (old mean + 6) x 2.5 = 30 x 2.5 = 75.

Multiple choice

\text{Find the value of both quantities and then state the correct relationship.}\\text{Quantity I: } \text{largest number if the average of 7 consecutive odd no. is 53}\\text{Quantity II:} \text{ largest number if the avg of 6 consecutive odd no. is 56}

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For consecutive odd numbers with average 53 (7 numbers): The middle (4th) number is 53. Numbers are 47, 49, 51, 53, 55, 57, 59. Largest = 59. For consecutive odd numbers with average 56 (6 numbers): Average lies between 3rd and 4th numbers. Numbers are 51, 53, 55, 57, 59, 61. Largest = 61. Quantity II (61) > Quantity I (59). This confirms answer C is correct. The topic as 'Number Series' is appropriate.

Multiple choice

Average of n numbers is X. If 36 is decreased from two numbers, the new average becomes (x - 8). What is the value of n?

  1. 2

  2. 4

  3. 6

  4. 8

  5. 9
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

When total of n numbers decreases by 72 (36 from two numbers), the average decreases by 8. Using the formula: Total decrease = n × (decrease in average). Therefore: 72 = n × 8, which gives n = 9. The correct answer is 9, which corresponds to option E. Options A, B, C, and D are all incorrect.

Multiple choice

In a survey conducted by a group of students on 20 households in a local area, the following frequency table has been obtained related to the number of household family members: Size of the family Number of families 1 – 3 7 3 – 5 9 5 – 7 2 7 – 9 1 9 – 11 1 Find the mode of these observations.

  1. 3.571

  2. 3.286

  3. 3.628

  4. 3.444
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For grouped frequency data, the mode is calculated using: Mode = L + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h, where L is lower limit of modal class, f₁ is frequency of modal class, f₀ is frequency of preceding class, f₂ is frequency of succeeding class, h is class width. Modal class is 3-5 (highest frequency 9). Mode = 3 + [(9-7) / (2×9-7-2)] × 2 = 3 + [2/9] × 2 = 3 + 4/9 = 3.444. The claimed answer D is correct.

Multiple choice

The mean of observations 2, x, 7, 3, y, 9, 6 is 6, where x and y are constants. If x is replaced by 3x + 1 and y is replaced by y + 3, then the mean increases by 2. Find the value of x.

  1. 7

  2. 5

  3. 10

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original mean is 6 for 7 observations, so sum = 42. This gives x + y = 15. After replacements, new sum = 56 (mean increases by 2 to 8). This gives 3x + y = 25. Subtracting the two equations: 2x = 10, so x = 5. You can verify by finding y = 10 and checking both conditions are satisfied.

Multiple choice

The mean of the 8 smallest numbers in a group is 17, while taking together the mean of all the numbers in the group is 20. If the mean of the remaining numbers after leaving the smallest eight numbers is 22, then how many numbers are there in the group?

  1. 18

  2. 20

  3. 22

  4. 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let there be n numbers total. Sum of 8 smallest = 8 × 17 = 136. Sum of all numbers = n × 20. Sum of remaining (n-8) numbers = (n-8) × 22. Total sum = 136 + (n-8) × 22 = 20n. Solving: 136 + 22n - 176 = 20n, giving 2n = 40, so n = 20. Option B is correct. Option A (18) and D (19) don't satisfy the equation.

Multiple choice

In a class, there were 9 boys and some girls. In a test the mean score obtained by boys was 12 while that obtained by the girls was 14. If the overall average was 13.1, what was the total number of students in the class?

  1. 21

  2. 19

  3. 22

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let number of girls = g. Total score = 9×12 + g×14 = 108 + 14g. Total students = 9 + g. Average = (108 + 14g)/(9 + g) = 13.1. Solving: 108 + 14g = 117.9 + 13.1g, so 0.9g = 9.9, giving g = 11. Total students = 9 + 11 = 20.

Multiple choice

The average of a group of 18 numbers is 37.5. If 6 numbers of average x are added to them, then the average of all the numbers increases by 1. Then find the value of x is?

  1. 41.5

  2. 40

  3. 42

  4. 38.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of 18 numbers = 18 × 37.5 = 675. Sum of 6 new numbers = 6x. New sum = 675 + 6x. New average = (675 + 6x)/24 = 38.5. Solving: 675 + 6x = 924, which gives 6x = 249, so x = 41.5. This is a straightforward average problem where the new average is given as 38.5 (37.5 + 1).