Tag: range and mean deviation

Questions Related to range and mean deviation

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

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

  1. $47$

  2. $24$

  3. $44$

  4. $50$

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Correct Option: D
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 $\dfrac{SD}{AM}\times100=\dfrac{10}{20}\times100=50\%$

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

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

  1. $57.7\%$

  2. $45.7\%$

  3. $35.7\%$

  4. None of these

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Correct Option: C
Explanation:

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

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

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

  1. $12$

  2. $0.12$

  3. $20$

  4. $120$

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Correct Option: A
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.

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

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

  1. $20$

  2. $25$

  3. $30$

  4. $35$

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Correct Option: B
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 $=\dfrac{\sigma}{\overline{x}}\times 100$

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

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

Coefficient of deviation is calculated by the formula:

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

  1. $\cfrac { \bar { X } }{ \sigma } \times 100$

  2. $\cfrac { \bar { X } }{ \sigma }$

  3. $\cfrac { \sigma } {\bar { X }} \times 100$

  4. $\cfrac{ \sigma } { \bar { X }}$

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Correct Option: C
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.

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

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

  1. 20

  2. 40

  3. 30

  4. none of these

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Correct Option: C
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

The range of the data 
25,18,20,22,16,6,17,12,30,32,10,19,8,11,20 is

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

  1. $20$

  2. $16$

  3. $18$

  4. $26$

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Correct Option: D
Explanation:

The range of the data=Highest vale-lowest value

Highest value= 36
Lowest value=6
$\therefore$Range of the data=$32-6=24$

The difference between the maximum and the minimum observation in the data is

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

  1. class interval

  2. frequency

  3. cumulative frequency

  4. range

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Correct Option: D
Explanation:

Range =maximum value-minimum value

Hence range is the difference between the maximum and the minimum  observation.

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

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

  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

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Correct Option: B
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 $\text{coefficient of range}=\dfrac{a-b}{a+b}=\dfrac{range}{a+b}$

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

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

  1. $3.38$kg.

  2. $2.38$kg.

  3. $6.38$kg.

  4. None of these

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Correct Option: A
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 $3.38\,kg$