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

A teacher gave a sum to his class to find the average of 'n' number wiz 1, 2, 3, ... n. But when the teacher checked the solution, he found that during calculation, a student just missed a number for addition and thus his average of 'n' numbers was 15. The least value of n is

  1. n = 29

  2. n = 30

  3. n = 31

  4. n = 32
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of 1 to n is n(n+1)/2. The average is (n+1)/2. If one number x (where 1 <= x <= n) is missed, the new average is (n(n+1)/2 - x) / (n-1) = 15. For n=30, sum is 465. (465-x)/29 = 15 implies 465-x = 435, so x = 30. Since 30 is a valid number in the set, n=30 is correct.

Multiple choice

The average of ten consecutive numbers is n. If the next ten numbers are also included, the average increases by 50%. What is the value of n?

  1. 5

  2. 10

  3. 15

  4. 20

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be x, x+1, ..., x+9. Average n = x + 4.5. If 10 more numbers are added (x+10 to x+19), the new average is (sum of 20 numbers) / 20 = (20x + 190) / 20 = x + 9.5. Given x + 9.5 = 1.5 * n = 1.5 * (x + 4.5) = 1.5x + 6.75. So 0.5x = 2.75 => x = 5.5. n = 5.5 + 4.5 = 10.

Multiple choice

If the mean of the following frequency distribution is 2.7, and total of frequencies is 20, then find x and y. | Data | 1 | 2 | 3 | 4 | 5 | | --- | --- | --- | --- | --- | --- | | Frequency | 5 | x | 4 | 3 | y |

  1. 7, 1

  2. 6, 2

  3. 5, 3

  4. 4, 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total frequency = 5 + x + 4 + 3 + y = 20, so x + y = 8. Mean = (1*5 + 2*x + 3*4 + 4*3 + 5*y) / 20 = 2.7. 5 + 2x + 12 + 12 + 5y = 54. 2x + 5y = 25. Solving the system: x = 8 - y, so 2(8-y) + 5y = 25 => 16 + 3y = 25 => 3y = 9 => y = 3. Then x = 5.

Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and that of the females, 120 pounds. What is the average weight of the people in the group? (1) The group contains twice as many females as males. (2) The group contains 10 more females than males.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be the number of males and F be the number of females. Average weight = (180M + 120F) / (M + F). Statement (1) says F = 2M. Substituting gives (180M + 120(2M)) / (M + 2M) = (180 + 240) / 3 = 140. This is sufficient. Statement (2) says F = M + 10, which leaves M unknown, so it is not sufficient.

Multiple choice

Directions: The following problem consists of a question and two statements, labelled (A) and (B), in which certain data is given. You have to consider the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in June or the meaning of counterclockwise) and then decide which out of these four options is correct for the given question. To earn a grade B in her English class, Esha must have an average score of 75 in her exams. She has taken four exams so far. What score must she get in the fifth exam to have an average of 75? (A) She averaged 70 in her first four exams. (B) If she gets an 80 in the fifth exam, her average will be 72.

  1. Statement (A) alone is sufficient, but statement (B) alone is not sufficient to answer the question asked.

  2. Statement (B) alone is sufficient, but statement (A) alone is not sufficient to answer the question asked.

  3. Both statements (A) and (B) together are sufficient to answer the question asked, but neither statement alone is sufficient.

  4. Each statement alone is sufficient to answer the question asked.

  5. Statements (A) and (B) together are not sufficient to answer the question asked, and additional data relevant to the problem is needed.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Target average = 75 for 5 exams, so total score = 375. (A) Average of 4 exams = 70, so sum = 280. 5th exam = 375 - 280 = 95. Sufficient. (B) If 5th = 80, average = 72. Total = 72 * 5 = 360. Sum of 4 exams = 360 - 80 = 280. 5th exam = 375 - 280 = 95. Sufficient.

Multiple choice

The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean scroe of 80 and the dullest 25% secured a mean score of 31. The mean score of remaining 55% is :

  1. 50%

  2. 51.4% approx

  3. 54.6% approx

  4. 45%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using weighted average: Total score = 52×100 = 5200. Brightest 20% (20 students) score = 80×20 = 1600. Dullest 25% (25 students) score = 31×25 = 775. Remaining 55% (55 students) score = 5200-1600-775 = 2825. Mean of remaining = 2825/55 = 51.36 ≈ 51.4%. The key insight is balancing the weighted contributions of all subgroups.

Multiple choice

The mean of 20 items is 47. Later it is found that the item 62 is wrongly written as 26. Find the correct mean. 20 मदों का औसत 47 है। बाद में पता चला कि एक मद को 62 के स्थान पर गलती से 26 लिख दिया गया। तद्नुसार सही औसत ज्ञात कीजिए।

  1. 49.9

  2. 47.7

  3. 48.8

  4. 46.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The incorrect mean (47) was calculated with 26 instead of 62. Total sum with error = 47 × 20 = 940. Correct sum = 940 - 26 + 62 = 976. Correct mean = 976/20 = 48.8. Alternatively: difference in value = 62 - 26 = 36, so difference in mean = 36/20 = 1.8. Correct mean = 47 + 1.8 = 48.8.

Multiple choice

Mean of 10 numbers is 30. Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32. The correct mean is – 10 सख्ंयाओं का औसत 30 है । बाद में पता चलता है कि उनमें से दो संख्यायें 15, 23 के स्थान पर गलती से 51, 32 लिख दी गयी थी। तो सही औसत है –

  1. 25.5

  2. 32

  3. 30

  4. 34.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mean of 10 numbers is 30, so sum = 10 × 30 = 300. The wrong numbers 51 and 32 should be replaced by correct numbers 15 and 23. Correct sum = 300 - 51 - 32 + 15 + 23 = 300 - 83 + 38 = 255. Therefore correct mean = 255/10 = 25.5.