Tag: measures of dispersion and skewness

Quizzes (4) Questions (166)

Questions Related to measures of dispersion and skewness

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 standard deviation of $10, 16, 10, 16, 10, 10, 16, 16$ is?

  1. $4$
  2. $6$
  3. $3$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Assume $A=13;$ hence $d=A-13$

x d $d^2$
$10$ $-3$ $9$
$16$ $3$ $9$
$10$ $-3$ $9$
$16$ $3$ $9$
$10$ $-3$ $9$
$10$ $-3$ $9$
$16$ $-3$ $9$
$16$ $3$ $9$
$\displaystyle\sum d=0$ $\displaystyle\sum d^2=72$

Use following formula:
$\sqrt{\displaystyle\frac{\displaystyle\sum d^2}{n}-\left[\displaystyle\frac{\displaystyle\sum d}{n}\right]^2}$
$\sqrt{\displaystyle\frac{72}{8}-\left[\displaystyle\frac{0}{8}\right]^2}$
$\sqrt{9}$
$=3$.

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

Calculate standard deviation of the following data.

X $10$ $11$ $12$ $13$ $14$ $15$ $16$ $17$ $18$
f $2$ $7$ $10$ $12$ $15$ $11$ $10$ $6$ $3$
  1. $3.95$
  2. $1.99$
  3. $14$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
X f fx X-Mean $f(X-x)^2$
$10$ $2$ $20$ $-4$ $32$
$11$ $7$ $77$ $-3$ $63$
$12$ $10$ $120$ $-2$ $40$
$13$ $12$ $156$ $-11$ $2$
$14$ $15$ $210$ $0$ $0$
$15$ $11$ $165$ $1$ $11$
$16$ $10$ $160$ $2$ $40$
$17$ $6$ $102$ $3$ $54$
$18$ $3$ $54$ $4$ $48$
Total $76$ $fX=1064$ $f(X-X)^2=300$

$^-{X}=\displaystyle\frac{1064}{76}=14$
$\sigma x=\sqrt{\displaystyle\frac{300}{76}}$
$=\sqrt{3.95}$
$=1.99$.

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 the mean and standard deviation of the following observations: X $=2, 5, 7, 8, 13$.

  1. $7$ & $3.63$
  2. $3.63$ & $7$
  3. $7.63$ & $3$
  4. $3$ & $7.63$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle\frac{2+5+7+8+13}{5}=7$
$\sqrt{\displaystyle\frac{4+25+49+64+169}{5}}-49=3.63$.

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 the present value of Rs. $10,000$ to be required after $5$ years if the interest rate be $9\%$. Given that $(1.09)^5=1.5386$.

  1. $6,994.42$
  2. $6,949.24$
  3. $6,449.24$
  4. $6,499.42$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $i=0.09=9\%$
$n=5$
$A _n=10,000$
Required present value $=\displaystyle\frac{A _n}{(1+i)^n}$
$=\displaystyle\frac{10,000}{(1+0.09)^5}$
$=Rs. 6499.42$.

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 the standard deviation of the numbers $2,3,a$ and $11$ is $3.5,$ then which of the following is true?

  1. $3a^2-32a+84=0$
  2. $3a^2-34a+91=0$
  3. $3a^2-23a+44=0$
  4. $3a^2-26a+55=0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Numbers are $2,3,a$ and $11$
$N=4$
Standard deviation $\sigma=3.5$
Mean of numbers $(\overline{x})=\dfrac{2+3+11+a}{4}=\dfrac{16+a}{4}$

$\Rightarrow$  $\sigma^2=\dfrac{1}{N}\sum(x _i-\overline{x})^2$
$\Rightarrow$  $3.5\times 3.5\times 4\times  16=(8+a)^2+(4+a)^2+(16-3a)^2+(a-28)^2$
$\Rightarrow$  $784=64+a^2+16a+16+a^2+8a+256+9a^2-96a+a^2+784-56a$
$\Rightarrow$  $784=12a^2-128a+1120$
$\Rightarrow$  $196=3a^2-32a+280$

$\Rightarrow$  $3a^2-32a+84=0$

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 two observations $A$ & $B$ are given by $100, 101, ........149$ and $200, 201, .......,249$ with $V _{A}$ and $V _{B}$ are variances of $A$ and $B$ than $V _{A}$ is equal to :

  1. $V _{B}$
  2. $100\ V _{B}$
  3. $50\ V _{B}$
  4. $200\ V _{B}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\sigma {x^2} = \frac{{\sum {{d^2}} }}{h}${here deviation are taken  from mean}

Since, A and B have consecutive integers therefore both have same standard deviation and hence variation 
${ V _{ A } }={ V _{ B } }\sum { { d^{ 2 } }\, \, is\, \, same } $

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

In expected rate of return for constant growth, dividends are expected to grow but with the _____________.

  1. constant rate

  2. variable rate

  3. yielding rate

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

In the constant growth dividend discount model, dividends are assumed to grow at a stable, constant rate indefinitely.

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 the standard deviation of the values $2,4,6,8$ is $2.33$, then the standard deviation of the values $4,6,8,10$ is

  1. $0$
  2. $2.58$
  3. $4.66$

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

Given data values are $4,6,8,10$


Mean of the data is $\dfrac{4+6+8+10}{4}=\dfrac{28}{4}=7$

Therefore standard deviation is $\sqrt{\dfrac{(4-7)^2+(6-7)^2+(8-7)^2+(10-7)^2}{4-1}}=\sqrt{\dfrac{20}{3}}=2.58$

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 $24$.