Tag: variance and standard deviation

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Questions Related to variance and standard deviation

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

If the coefficient of variation and standard deviation of a distribution are 50% and 20 respectively, the its mean is

  1. 40

  2. 30

  3. 20

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

We know if a distribution having mean $\bar{x}$ and standard deviation $\sigma$
then coefficient of variation $=\cfrac{\sigma}{\bar{x}}\times 100$
$\therefore \cfrac{20}{\bar{x}}\times 100=50\Rightarrow \bar{x} = 40$
Hence required mean is $=40$

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

The sum of the squares of deviation of 10 observations from their mean 50 is 250, then coefficient of varition is

  1. 10%

  2. 40%

  3. 50%

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

Given $\displaystyle \Sigma \left ( x _{i}-\overline{x} \right )^{2}=250$,$n=10,\overline{x}=50$

Now, $\sigma=\sqrt{\dfrac{1}{n}\Sigma \left ( x _{i}-\overline{x} \right )^{2}}$

$= \sqrt{\dfrac{1}{10}\times 250}=5$ 
Hence coefficient of variation $\displaystyle =\dfrac{\sigma }{\overline{x}}\times 100=\dfrac{5}{50}\times 100=10$%

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

The sum of the squares of deviation of 10 observations from their mean 50 is 250, then coefficient of variation is

  1. 10%

  2. 40%

  3. 50%

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,   $\sum (x-\bar{x})^2 = 250, n = 10, \bar{x} =50$
Thus standard deviation $ = \sqrt{\cfrac{\sum (x-\bar{x})^2}{n}}=\sqrt{25}=5$
$\therefore$ Coefficient of variation $=\cfrac{\sigma}{\bar{x}}\times 100 =\cfrac{5}{50}\times 100$ % $= 10$%

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

The mean of a distribution is 4. If its coefficient of variation is 58%. Then the S.D. of the distribution is

  1. 2.23

  2. 3.23

  3. 2.32

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

Given,  mean $\bar{x} = 4,$ and coefficient of variation $=58$ %
If S.D of the given distribution is $\sigma$ then we know that,
Coefficient of variation $=\cfrac{\sigma}{\bar{x}}\times 100$ %
$\Rightarrow 58 = \cfrac{\sigma}{4}\times 100\Rightarrow \sigma = \cfrac{58\times 4}{100}=2.32$

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

For the given data, SD $= 10$, AM $= 20$ the coefficient of variation is ...........

  1. $47$
  2. $24$
  3. $44$
  4. $50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Coefficient of variation is the ratio of standard deviation to the mean.


Given that $SD=10$ and $AM=20$

Therefore of coefficient of variation is $\dfrac{SD}{AM}\times100=\dfrac{10}{20}\times100=50\%$

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

The mean of a distribution is $14$ and standard deviation is $5$. What is the value of the coefficient of variation?

  1. $57.7\%$
  2. $45.7\%$
  3. $35.7\%$

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

Coefficient of variation is given by $CV = \dfrac{SD}{Mean}\times 100 $
$\Rightarrow \dfrac{5}{14}\times 100 = 35.7\%$

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

If the standard deviation of a set of scores is $1.2$ and their mean is $10$, then the coefficient of variation of the scores is

  1. $12$
  2. $0.12$
  3. $20$
  4. $120$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given : standard deviation$(\sigma)=1.2,$ mean$(\overline {X})=10$.

Coefficient of variation(C.V.) $=\dfrac{\sigma}{\overline {X}}\times 100=\dfrac{1.2}{10}\times 100=12$
$\therefore$ C.V. $=12$
Hence, option $A$ is correct.

Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

If $n=10, \bar{x}=12$ and $\sum x^2=1530$, then calculate the coefficient of variation.

  1. $20$
  2. $25$
  3. $30$
  4. $35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\sigma=\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{\sum x}{n}\right)^2}$

   
   $=\sqrt{\dfrac{1530}{10}-(12)^2}$

   $=\sqrt{153-144}$
   $=\sqrt{9}$
   $=3$

Coefficient of variation $=\dfrac{\sigma}{\overline{x}}\times 100$

                                       $=\dfrac{3}{12}\times 100$

                                       $=\dfrac{1}{4}\times 100$
                                       $=25$

Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

Coefficient of deviation is calculated by the formula:

  1. $\cfrac { \bar { X } }{ \sigma } \times 100$
  2. $\cfrac { \bar { X } }{ \sigma }$
  3. $\cfrac { \sigma } {\bar { X }} \times 100$
  4. $\cfrac{ \sigma } { \bar { X }}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

It is a fundamental concept.
coefficient of deviation $=\cfrac{\sigma}{\bar{x}}\times 100$
where $\sigma$ and $\bar{x}$ are standard deviation and mean respectively.