Tag: measures of dispersion

Quizzes (8) Questions (118)

Questions Related to measures of dispersion

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

What are the advantages of squaring a difference for calculating variance and standard deviation?

  1. Squaring makes each term positive so that values above the mean do not cancel below the mean.

  2. Squaring adds more weight to the larger differences, and in many cases this extra weight is appropriate since points further from the mean may be more significant.

  3. It complicates the calculations

  4. All are incorrect
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

Since,

$\sigma _x=\sqrt{\cfrac{\sum (x _i-\bar x)^2}{N}}$
So, we can say that opion $A$ and $B$ are correct.

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

Which of the following are positional measure of dispersion?

  1. Standard Deviation, Variance

  2. Percentile, Variance

  3. Quartile, Variance

  4. Percentile,Quartile
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Percentile,Quartile are positional measure of dispersion because it tells about the position of a particular data value has within a data set.
Standard deviation, Variance are computational measure of dispersion.

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, then 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

Given $\sigma = 20$, coefficient of variation $=50$ %
We know coefficient of variation $=\cfrac{\sigma }{\bar{x}}\times 100=50$
$\Rightarrow \bar{x} = 2\times \sigma = 40$

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

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250 $. Then Co-efficient of variation is

  1. $10\%$
  2. $40\%$
  3. $50\%$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\sum(x-\overline{x})^2=250$, $\overline{x}=50$
$\Rightarrow$  Standard deviation $(\sigma)=\sqrt{\dfrac{250}{10}}=\sqrt{25}=5$
$\Rightarrow$  Coefficient of variation $=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}}$
                                             $=\dfrac{\sigma}{Mean}\times 100$

                                             $=\dfrac{5}{50}\times 100$

                                             $=10\%$
Multiple choice maths measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

The Coefficient of Variation is given by:

  1. $\dfrac{Mean}{\ Standard \ \ deviation } \times 100$
  2. $\dfrac{\ Standard \ \ deviation }{Mean}$
  3. $\dfrac{Standard \ \ deviation }{Mean }\times 100$
  4. $\dfrac{Mean}{Standard \ Deviation}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The coefficient of variation (CV) is a standardized measure of dispersion 

. It is defined as the ratio of the standard deviation to the mean.
$CV\quad =\quad \cfrac { \sigma  }{ Mean }\times100 $

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

If mean of a series is 40 and variance 1486, then coefficient of variation is 

  1. $0.9021$
  2. $0.9637$
  3. $0.8864$
  4. $0.9853$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If mean of the given dist. be $\bar{x}$ and S.D be $\sigma $
then given $\bar{x} = 40, \sigma^2 = 1486$
$\therefore$ Coefficient of variation $=\cfrac{\sigma}{\bar{x}}=\cfrac{\sqrt{1486}}{40}=.9637$

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 $=\cfrac{\sigma}{\bar{x}}\times 100$ %
$\Rightarrow 58 = \cfrac{\sigma}{4}\times 100\Rightarrow \sigma = \cfrac{58\times 4}{100}=2.32$