Mathematics · Quantitative Aptitude

Statistics and Dispersion

515 Questions

Statistics and dispersion involve the calculation of mean, standard deviation, variance, and coefficient of variation for data sets. These questions also cover probability distributions and cumulative frequency analysis. Such quantitative aptitude topics are heavily featured in banking and SSC examinations.

Standard deviationNormal distributionMean calculationCumulative frequencyCoefficient of variation

Statistics and Dispersion Questions

Multiple choice

Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P (X ≤ -1) = P (Y ≥ 2)$ , the standard deviation of $Y$ is

  1. 3

  2. 2
  3. $\sqrt{2}$

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X (1,4),4(-1,$\sigma^2$) P(x $\le$-1) Z = $\dfrac{-1-1}{2}$ = -1 = P (Z $\le$ -1) = P (Z $\ge$1) = 0.5 - P (0<z<1) = 0.1587 If $\sigma$= 3 then P(Z $\ge$ 2), Z = $\dfrac{2+1}{3}$= 1 = P (Z $\ge$1) = 0.1587

Multiple choice

Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$. Let $\mu_x$ be the mean and $\sigma_x$ be the standard deviation of $X$. Let another finite sequence $Y$ of equal length be derived from this as $y_i=a*x_i+b$, where $a$ and $b$ are positive constants. Let $\mu_y$ be the mean and $\sigma_y$ be the standard deviation of this sequence. Which one of the following statements is INCORRECT?
  1. ndex position of mode of $X$ in $X$ is the same as the index position of mode of $Y$ in $Y$
  2. ndex position of median of $X$ in $X$ is the same as the index position of median of $Y$ in $Y$
  3. $\mu_y=a \mu_x + b$
  4. $\sigma_y=a \sigma_x + b$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For linear transformation Y = aX + b: mean scales as μ_y = aμ_x + b (shifts and stretches). Standard deviation scales as σ_y = aσ_x (only stretches, not shifts). Option D incorrectly adds b to standard deviation - this is wrong because b is a constant shift and doesn't affect spread. Options A and B about mode/median index positions are correct (order statistics preserved under linear transforms). Option C about mean is correct.

Multiple choice

Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list. Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list. R: Doubling each entry in a list doubles the mean of the list. S: Doubling each entry in a list leaves the standard deviation of the list unchanged.

  1. P, Q

  2. Q, R

  3. P, R

  4. R, S
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P and R always hold true. Otherwise, consider a sample set {1, 2, 3, 4} and check accordingly.