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 following data shows the number of goals scored by different number of players in a tournament. Find the mean deviation about mean. Number of goals Number of players 0-3 2 3-6 4 6-9 2 9-12 2

  1. 2.64

  2. 1.5

  3. 5.7

  4. 2.5

  5. NA
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Class intervals: 0-3, 3-6, 6-9, 9-12. Midpoints (x): 1.5, 4.5, 7.5, 10.5. Frequencies (f): 2, 4, 2, 2. Total N = 10. Mean = (1.5*2 + 4.5*4 + 7.5*2 + 10.5*2) / 10 = (3 + 18 + 15 + 21) / 10 = 5.7. Mean deviation = Sum(f * |x - mean|) / N = (2*|1.5-5.7| + 4*|4.5-5.7| + 2*|7.5-5.7| + 2*|10.5-5.7|) / 10 = (2*4.2 + 4*1.2 + 2*1.8 + 2*4.8) / 10 = (8.4 + 4.8 + 3.6 + 9.6) / 10 = 26.4 / 10 = 2.64.

Multiple choice

The sum of deviations from 50 of n values x1, x2, ... xn is -10 and the sum of deviations from 46 of x1, x2, ... xn is 70. Then the deviation of the mean of the given values from 48 is

  1. 1.5

  2. -1.5

  3. 2

  4. -2.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of deviations from A is sum(x_i - A) = sum(x_i) - nA. For A=50, sum(x_i) - 50n = -10. For A=46, sum(x_i) - 46n = 70. Subtracting equations: 4n = 80, so n = 20. Then sum(x_i) = 990. Mean = 990/20 = 49.5. Deviation from 48 = 49.5 - 48 = 1.5.

Multiple choice

Directions : Select the correct alternative from the given choices. There are five positive integers. When any four of these integers are considered and their average is added to the fifth integer, we get the following numbers: 41, 44, 50, 56 and 65. Which of the following gives the value of one of these five integers?

  1. 28

  2. 44

  3. 36

  4. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be x1, x2, x3, x4, x5. Let S = x1+x2+x3+x4+x5. The given values are (S-xi)/4 + xi = 41, 44, 50, 56, 65. This simplifies to S + 3xi = 164, 176, 200, 224, 260. Summing these: 5S + 3S = 1024, so 8S = 1024, S = 128. 3xi = 164-128=36 => xi=12; 176-128=48 => xi=16; 200-128=72 => xi=24; 224-128=96 => xi=32; 260-128=132 => xi=44.

Multiple choice

Directions: Select the correct alternative from the given choices. Three persons, A, B and C, have a certain number of chocolates with each of them. The number of chocolates with B is 20% more than that with A, which, in turn, is two-thirds of that with C. If the number of chocolates with B is less than the total number of chocolates with A and C together by x percent, what is the value of x?

  1. 30

  2. 40

  3. 48

  4. 52
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A = 2, then C = 3 (since 2 is 2/3 of 3). B is 20% more than A, so B = 2 * 1.2 = 2.4. Total of A and C is 2 + 3 = 5. B is 2.4, which is 2.6 less than 5. The percentage x is (2.6 / 5) * 100 = 52%.