Tag: measures of dispersion

Quizzes (8) Questions (118)

Questions Related to measures of dispersion

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

If $y=-8x-5$ and SD of $x$ is $3$, then SD of $y$ is:

  1. $8$
  2. $24$
  3. $3$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given that std dev of x is $\sigma(x)=3$
Given equation is $y=-8x-5$

applying std dev on both sides we get

$\sigma(y)=\sigma(-8x-5)$

$\implies \sigma(y)=\sigma(-8x)+\sigma(-5)$

$\implies \sigma(y)=\sigma(-8x)+0$ (since, $\sigma(c)=0$)

$\implies \sigma(y)=8\sigma(x)$ (since, $\sigma(aX)=|a|\sigma(X)$)

$\implies \sigma(y)=8\times 3=24$

Therefore, standard deviation of $y$ is $24$.
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Suppose for $40$ observations, the variance is $50$. If all the observations are increased by $20$, the variance of these increased observation will be

  1. $20$
  2. $50$
  3. $30$

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

The variance for $40$ observations is $50$
Variance is independent of the number of observations. Therefore, variance for $60$ observations is $50$

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The variance of $5$ numbers is $10$. If each number is divided by $2$, then the variance of new numbers is

  1. $5.5$
  2. $2.5$
  3. $5$

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

Given that variance of $5$ number is $10$


Therefore, $Var(X)=10$

Given that each number is divided by $2$

Therefore, variance of new numbers is $Var(\dfrac X2)$

$Var(\dfrac X2)=\dfrac 14Var(X)=\dfrac 1 4(10)=2.5$

Hence, variance of new numbers is $2.5$

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Find $Var(2X+3)$

  1. $5 Var(X)+3$
  2. $4 Var(X)+3$
  3. $4 Var(X)$

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

$Var(2X+3)=Var(2X)+Var(3)$


$\implies Var(2X+3)=Var(2X)+0$ (Since, $Var(c)=0$)

$\implies Var(2X+3)=2^2Var(X)$ (Since, $Var(aX)=a^2Var(X)$)

$\implies Var(2X+3)=4Var(X)$

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

If a, b are constants then, $Var(a+bX)$ is

  1. $Var(a)+Var(X)$
  2. $Var(a)-Var(X)$
  3. $b^2Var(X)$

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

$Var(a+bX)=Var(a)+Var(bX)$


$\implies Var(a+bX)=0+Var(bX)$ (Since, $Var(c)=0$)

$\implies Var(a+bX)=b^2Var(X)$ (Since, $Var(aX)=a^2Var(X)$)

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The variance of $20$ observations is $5$. If each observation is multiplied by $2$, then what is the new variance of the resulting observations?

  1. $5$
  2. $10$
  3. $20$
  4. $40$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If each observation is multiplied by $2$, then mean$(\mu )$ will get doubled.

Now, variance $=\sigma ^{ 2 }=\dfrac { (X-\mu )^{ 2 } }{ n } $
Now here both $X$ and $\mu $ will be doubled, so the variance will become four times.
Thus, the new variance will be $4$ times the older variance which is $4\times 5=20$.
Hence, C is correct.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The formula Of $X^2$ distribution is______________.

  1. ${X^2} = \dfrac {{S}^{2} _{1}}{{S}^{2} _{2}}$
  2. ${X^2} = \dfrac {E}{{\Sigma}(O - E)^2}$
  3. ${X^2} = {\Sigma} \dfrac {E}{(E - O)^2}$
  4. ${X^2} = {\Sigma} \dfrac {(O - E)^2}{E}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The correct formula for Chi square distribution is given in option D, where O means the observed number in the table and E means the corresponding expected number.