Tag: business economics and quantitative methods

Quizzes (24) Questions (932)

Questions Related to business economics and quantitative methods

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 A.M of a set of observations is $9$ and its G.M is $6$. Then the H.M of the set of observations is ____.

  1. $4$
  2. $6$
  3. $3$

  4. None of them
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For any set of positive numbers, the relationship between Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM) is GM^2 = AM * HM. Given AM=9 and GM=6, then 36 = 9 * HM, so HM = 4.

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

To find the median, it is necessary to arrange the data in _______.

  1. ascending order

  2. descending order

  3. ascending or descending order

  4. any of them
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the median, the data must be ordered by magnitude, which can be done in either ascending or descending order.

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 $0-10$ $10-20$ $20-30$ $30-40$ $40-50$
f $10$ $8$ $15$ $8$ $4$
  1. $-12$
  2. $12$
  3. $12.36$
  4. $152.77$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Marks Mid-values(X) f dxi$=X-25/10$ $fdx _if$ $dx _i^2$
$0-10$ $5$ $10$ $-2$ $-20$ $40$
$10-20$ $15$ $8$ $-1$ $-8$ $8$
$20-30$ $25$ $15$ $0$ $0$ $0$
$30-40$ $35$ $8$ $1$ $8$ $8$
$40-50$ $45$ $4$ $2$ $8$ $16$
Total $45$ $-12$ $72$

$\sqrt{\displaystyle\frac{72}{45}-\frac{144}{45\times 45}}\times 10$
$=12.36$

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.