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

Let $\mathrm{x}{1},\ \mathrm{x}{2},...........,\ \mathrm{x}{\mathrm{n}}$ be $\mathrm{n}$ observations such that $\displaystyle \sum \mathrm{x}{\mathrm{i}}^{2}=400$ and $\displaystyle \sum \mathrm{x}_{\mathrm{i}}=80$. Then a possible value of $\mathrm{n}$ among the following is
  1. $15$
  2. $18$
  3. $9$
  4. $12$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Variance = (Sum(xi^2)/n) - (Sum(xi)/n)^2. Since variance must be >= 0, (400/n) - (80/n)^2 >= 0. This simplifies to 400/n >= 6400/n^2, or 1 >= 16/n, so n >= 16. Among the choices, 18 is the only value >= 16.

Multiple choice

In a series of $2\mathrm{n}$ observations, half of them equal $a$ and remaining half equal $-a$. If the standard deviation of the observations is $2$, then $|\mathrm{a}|$ equals:
  1. $\displaystyle \frac{1}{\mathrm{n}}$
  2. $\sqrt{2}$
  3. $2$
  4. $\displaystyle \frac{\sqrt{2}}{\mathrm{n}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Observations: n of 'a' and n of '-a'. Mean = 0. Variance = [n(a^2) + n(-a)^2] / 2n = 2na^2 / 2n = a^2. Standard deviation = sqrt(variance) = |a|. Given SD = 2, so |a| = 2.

Multiple choice

In a final examination in Statistics the mean marks of a group of $150$ students were $78$ and the S.D was $8.0$. In Economics, however, the mean marks were $73$ and the S.S was $7.6$. The variability in the two subjects respectively is
  1. $10.3\%,10.4\%$
  2. $95\%,7.9\%$
  3. $11.2\%,10.1\%$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Variability here is the coefficient of variation, calculated as standard deviation divided by mean, multiplied by 100. The values are 8/78 x 100 = 10.3% and 7.6/73 x 100 = 10.4%, respectively.

Multiple choice

The variance of observations $112, 116, 120, 125, 132$ is
  1. $58.8$
  2. $48.8$
  3. $61.8$

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

Mean = (112+116+120+125+132)/5 = 605/5 = 121. Variance = [(112-121)^2 + (116-121)^2 + (120-121)^2 + (125-121)^2 + (132-121)^2] / 5 = (81 + 25 + 1 + 16 + 121) / 5 = 244 / 5 = 48.8.

Multiple choice

In a class of $100$ students, the mean marks obtained in a subject is $30$ and in another class of $50$ students, the mean marks obtained in the same subject is $60$. What is the mean marks obtained by the students of two classes taken together?
  1. $40$
  2. $45$
  3. $48$
  4. $50$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total marks for the first class is 100 * 30 = 3000. The total marks for the second class is 50 * 60 = 3000. The combined mean is (3000 + 3000) / (100 + 50) = 6000 / 150 = 40.