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

Marks distribution of 20 students of a class is as follows: Marks Number of students 0 – 5 2 5 – 10 1 10 – 15 8 15 – 20 2 20 – 25 7 What is the mode of the above given data?

  1. 12.69

  2. 12.00

  3. 17.69

  4. 18.32
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The modal class is 10-15 (frequency 8). Mode = L + ((f1 - f0) / (2*f1 - f0 - f2)) * h. L=10, f1=8, f0=1, f2=2, h=5. Mode = 10 + ((8-1) / (16-1-2)) * 5 = 10 + (7/13) * 5 = 10 + 35/13 = 10 + 2.69 = 12.69.

Multiple choice

Directions: In the following questions, out of the four alternatives, choose the one which can be substituted for the given words/sentence. The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25%, a mean score of 31. The mean score of remaining 55% is

  1. 54.6%

  2. 45%

  3. 50%

  4. 51.4%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Take the total number of students as 100. The top 20 contribute 1600 points and the bottom 25 contribute 775 points, leaving 2825 points for the remaining 55 students. Their mean is 2825/55 = 51.4, so the numerical answer matches option D, although the percent sign is inappropriate.

Multiple choice

The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, what will be the new mean and the new standard deviation, respectively?

  1. 45, 5

  2. 11.25, 1.25

  3. 11.25, 2.5

  4. 12.5, 2.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If each observation x is transformed to (x-a)/b, the new mean is (mean-a)/b and the new standard deviation is SD/|b|. Here a=5, b=4. New mean = (50-5)/4 = 45/4 = 11.25. New SD = 10/4 = 2.5.

Multiple choice

Students of three sections of a class, having 30, 30 and 40 students, respectively, appeared for a test of 100 marks. The arithmetic means of the marks of the three sections are 72.2, 69.0 and 64.1 in that order. What is the arithmetic mean of the marks of all the students of three sections?

  1. 66.6

  2. 67.3

  3. 68.0

  4. 70.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Weighted mean = (30*72.2 + 30*69.0 + 40*64.1) / (30+30+40) = (2166 + 2070 + 2564) / 100 = 6800 / 100 = 68.0.

Multiple choice

If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation:

  1. x2 - 20x + 18 = 0

  2. 2x2 - 20x + 19 = 0

  3. x2 - 10x + 18 = 0

  4. x2 - 10x + 19 = 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mean = (3+5+7+a+b)/5 = 5 => 15+a+b = 25 => a+b = 10. Variance = 2^2 = 4. Variance = [ (3-5)^2 + (5-5)^2 + (7-5)^2 + (a-5)^2 + (b-5)^2 ] / 5 = 4. 4 + 0 + 4 + (a-5)^2 + (b-5)^2 = 20 => (a-5)^2 + (b-5)^2 = 12. Using (a-5)^2 + (b-5)^2 = a^2+b^2 - 10(a+b) + 50 = 12. Since (a+b)^2 = a^2+b^2 + 2ab = 100, a^2+b^2 = 100-2ab. Substitute: 100-2ab - 100 + 50 = 12 => 2ab = 38 => ab = 19. Equation is x^2 - (a+b)x + ab = 0 => x^2 - 10x + 19 = 0.