Tag: range and mean deviation

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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.

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

For a symmetrical distribution lower quartitl is 20 and upper quartile is 40.The value of 50th percentile is

  1. 20

  2. 40

  3. 30

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

First quartile also called the lower quartile or the 25th percentile(splits off the lowest 25% of data from the highest 75%)
Second quartile also called the median or the 50th percentile (cuts data set in half)
Third quartile  also called the upper quartile or the 75th percentile (splits off the highest 25% of data from the lowest 75%)
Since its a symmetrical distribution therefore the median will be 30

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

The formula for the coefficient of range is $\dfrac{\text{Range}}{a+b}$. Here, $a$ and $b$ denote:

  1. the mean and median of the data set

  2. the maximum and the minimum value of the data set

  3. the mean and mode value of the data set

  4. the minimum and mean value of the data set
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Range is the difference between the maximum value and the minimum value of the data set.


Let $a$ be the maximum value of the data set and
$b$ be the minimum value of the data set

Therefore, $range = a-b$

Coefficient of range is the relative measure of the dispersion.

It is given by $\text{coefficient of range}=\dfrac{a-b}{a+b}=\dfrac{range}{a+b}$

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

The largest of $50$ measurements is $3.84$kg. If the range is $0.46$kg, find the smallest measurement.

  1. $3.38$kg.
  2. $2.38$kg.
  3. $6.38$kg.

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

$\Rightarrow$  Here, $L=3.84$ and $R=0.46$

$\Rightarrow$  $R=L-S$
  $0.46=3.84-S$
  $S=3.84-0.46$
$\therefore$  $S=3.38\,kg$
$\therefore$   Smallest measurement is $3.38\,kg$