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 mean deviation of the following data from mean is : Class interval 0-5 5-10 10-15 15-20 20-25 Frequency 3 4 8 10 5
  1. $5$
  2. $4$
  3. $6$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Midpoints (x): 2.5, 7.5, 12.5, 17.5, 22.5. Frequencies (f): 3, 4, 8, 10, 5. Sum(fx) = 7.5 + 30 + 100 + 175 + 112.5 = 425. Total f = 30. Mean = 425/30 = 14.16. Mean deviation = Sum(f|x - mean|) / Sum(f). Calculations: 3|2.5-14.16| + 4|7.5-14.16| + 8|12.5-14.16| + 10|17.5-14.16| + 5|22.5-14.16| = 35 + 26.6 + 13.3 + 33.4 + 41.7 = 150. 150 / 30 = 5.

Multiple choice

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

Observations: n of 'a' and n of '-a'. Mean = (n*a + n*(-a)) / 2n = 0. Variance = sum(x_i^2) / 2n - mean^2 = (n*a^2 + n*(-a)^2) / 2n = 2n*a^2 / 2n = a^2. Standard deviation = sqrt(a^2) = |a|. Given SD = 2, so |a| = 2.

Multiple choice

The mean deviation of items $ \displaystyle x, x + y, x + 2y, ... x + 2ny $ from mean is
  1. $ \displaystyle \frac{n\left ( n+1\right )y}{2n+1} $
  2. $ \displaystyle \frac{\left ( n+1\right )y}{2n+1} $
  3. $ \displaystyle\frac{ny}{2n+1} $
  4. $ \displaystyle\frac{\left ( 2n+1 \right )y} {n\left ( n+1 \right )} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The series is an arithmetic progression with 2n+1 terms: x, x+y, ..., x+2ny. The mean is x+ny. The mean deviation is the average of the absolute differences from the mean: (1/(2n+1)) * sum(|(x+ky) - (x+ny)|) for k=0 to 2n. This simplifies to (y/(2n+1)) * (sum(|k-n|)). The sum is 2 * (1+2+...+n) = 2 * (n(n+1)/2) = n(n+1). Thus, the mean deviation is n(n+1)y / (2n+1).

Multiple choice

The mean deviation from mean of observations 5, 10, 15, 20, ......85 is
  1. $43.71$
  2. $21.17$
  3. $38.7$

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

Mean of 5, 10, ..., 85 (17 terms) = (5+85)/2 = 45. Mean deviation = (1/17) * sum |xi - 45|. Sum = |5-45| + |10-45| + ... + |85-45| = 40 + 35 + 30 + 25 + 20 + 15 + 10 + 5 + 0 + 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 = 360. Mean deviation = 360 / 17 = 21.176.

Multiple choice

A group of 10 observations has mean 5 and S.D. $\displaystyle 2\sqrt{6}.$ Another group of 20 observations has mean 5 and S.D. $\displaystyle 3\sqrt{2},$ then the S.D. of combined group of 30 observations is
  1. $\displaystyle \sqrt{5}$
  2. $\displaystyle 2\sqrt{5}$
  3. $\displaystyle 3\sqrt{5}$

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

Combined mean = (10*5 + 20*5) / 30 = 5. Combined variance = (n1(s1^2 + d1^2) + n2(s2^2 + d2^2)) / (n1+n2), where d1 = mean1 - combined_mean = 0. Variance = (10*(24) + 20*(18)) / 30 = (240 + 360) / 30 = 600 / 30 = 20. SD = sqrt(20) = 2*sqrt(5).