Tag: measures of dispersion

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Questions Related to measures of dispersion

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

If the standard deviation of $x _{1},x _{2},.....x _{n}$ is 3.5, then the standard deviatiuon of $-2x _{1}-3,-2x _{2}-3....,-2x _{n}-3$ is

  1. -7

  2. -4

  3. 7

  4. 1.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standard deviation is independent of the change of origin (adding or subtracting a constant) and is scaled by the absolute value of the change of scale (multiplying by a constant). If the original SD is 3.5, the new SD is | -2 | * 3.5 = 7.

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

The variance of the data $6,\ 8,\ 10,\ 12\,,14\,,\ 16,\ 18,\ 20,\ 22,\ 24$ is

  1. $15$
  2. $20$
  3. $30$
  4. $33$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Mistake :$14$ is not given
Mean $\bar x=\dfrac{6+8+10+12+14+16+18+20+22+24}{10}=\dfrac{150}{10}=15$
Variance$=\dfrac{1}{n} \sum\limits _{i=1}^n(x _{i}-\bar x)^2$
$\implies \dfrac{1}{10}((6-15)^2+(8-15)^2+(10-15)^2+(12-15)^2+(14-15)^{2}+(16-15)^2+(18-15)^2+(20-15)^2$
$+(22-15)^2+(24-15)^2$

$\implies \dfrac{81+49+25+9+1+1+9+25+49+81}{10}$

$\implies \dfrac{330}{10}=33$
Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

The variate x and u are related by $\displaystyle u= \frac{x-a}{h}$ then correct relation between $\displaystyle \sigma _{x}:and:\sigma _{u}$

  1. $\displaystyle \sigma _{x}= h\sigma _{u}$
  2. $\displaystyle \sigma _{x}= h+\sigma _{u}$
  3. $\displaystyle \sigma _{u}= h\sigma _{x}$
  4. $\displaystyle \sigma _{u}= h+\sigma _{x}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given $\displaystyle u =\frac{x}{h}-\frac{a}{h}$
Since,S.D. is not depend on change of origin but it is depend on change of scale.
$\displaystyle \therefore \sigma _{u}=\frac{\sigma _{x}}{h}$
$\Rightarrow h\sigma _{u}=\sigma _{x}$

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

Standard deviation of a collection of data is $2\sqrt{2}$. If each value in a data set  is multipled by $3$, then the standard deviation of the new data is.

  1. $\sqrt{12}$
  2. $4\sqrt{2}$
  3. $6\sqrt{2}$
  4. $9\sqrt{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The standard deviation would also be multiplied by $3$.
Because the mean would also be $3x$ larger, the differences from the mean would be $3x$ larger too.
It is the same idea as if you were looking at your data set through an enlarging lens- everything would be $3x$ bigger, not only the data values, but also the mean, the differences from the mean, but just everything!
$\therefore$ the standard deviation becomes $2\sqrt{2}\times 3=6\sqrt{2}$