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

Find the mean of the following data: | Age group | 40 – 44 | 45 – 49 | 50 – 54 | 55 – 59 | 60 – 64 | 65 – 69 | | --- | --- | --- | --- | --- | --- | --- | | Number of people | 3 | 8 | 13 | 11 | 9 | 6 |

  1. 44.3

  2. 48.9

  3. 51.7

  4. 55.3

  5. 56.6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Midpoints (x): 42, 47, 52, 57, 62, 67. Frequencies (f): 3, 8, 13, 11, 9, 6. Sum (f*x): 126 + 376 + 676 + 627 + 558 + 402 = 2765. Total frequency = 50. Mean = 2765 / 50 = 55.3.

Multiple choice

What is the mean of the given data? | Class interval | 0 – 30 | 30 – 60 | 60 – 90 | 90 – 120 | 120 – 150 | 150 – 180 | | --- | --- | --- | --- | --- | --- | --- | | Frequency | 8 | 15 | 16 | 20 | 12 | 9 |

  1. 43

  2. 55

  3. 61

  4. 90

  5. 72
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Midpoints: 15, 45, 75, 105, 135, 165. Frequencies: 8, 15, 16, 20, 12, 9. Sum of f*x = 120 + 675 + 1200 + 2100 + 1620 + 1485 = 7200. Total frequency = 80. Mean = 7200 / 80 = 90.

Multiple choice

Read the following data and find the arithmetic mean. |||||||| |---|---|---|---|---|---|---| | (less than) x| 10| 20| 30| 40| 50| 60| | Frequency| 5| 20| 40| 58| 70| 100|

  1. 30.14

  2. 32.43

  3. 35.70

  4. 36.21
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Convert cumulative frequencies to class frequencies: 0-10 (5), 10-20 (15), 20-30 (20), 30-40 (18), 40-50 (12), 50-60 (30). Midpoints: 5, 15, 25, 35, 45, 55. Mean = (5*5 + 15*15 + 20*25 + 18*35 + 12*45 + 30*55) / 100 = (25 + 225 + 500 + 630 + 540 + 1650) / 100 = 3570 / 100 = 35.70.

Multiple choice

The mean and median of 5 observations are 9 and 8, respectively. If 1 is subtracted from each observation, then the new mean and the new median will, respectively be

  1. 8 and 7

  2. 9 and 7

  3. 8 and 9

  4. Cannot be determined due to insufficient data
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a constant is subtracted from each observation, the mean decreases by that constant and the median also decreases by that constant. New mean = 9 - 1 = 8. New median = 8 - 1 = 7.

Multiple choice

For a set of 100 observations taking assumed mean as 4, the sum of the deviations is -11 cm and the sum of squares of these deviations is 257 cm2. Find the coefficient of variation.

  1. 41.13%

  2. 14.13%

  3. 25.13%

  4. 52.13%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

N=100, A=4, Sum(d)=-11, Sum(d^2)=257. Mean = A + Sum(d)/N = 4 - 0.11 = 3.89. Variance = Sum(d^2)/N - (Sum(d)/N)^2 = 2.57 - (-0.11)^2 = 2.57 - 0.0121 = 2.5579. SD = sqrt(2.5579) = 1.599. CV = (SD/Mean)*100 = (1.599/3.89)*100 = 41.105%. Matches 41.13%.