Tag: statistics and probability

Questions Related to statistics and probability

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 $3.38\,kg$

The ________ is the difference between the greatest and the least value of the variate.

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

  1. Range

  2. Data

  3. Average

  4. Variance

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Correct Option: A
Explanation:

$Range$ $as$ $the$ $name$ $indicates$ $gives$ $us$ $all$ $the$ $area$ $available$ $under$ $light$ $and$ $hence$ $statement$ $is$ $true.$

The mean deviation from the median is _________ that measured from any other value.

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

  1. equal to 

  2. less than

  3. greater than

  4. None of these

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Correct Option: B
Explanation:

The value of the mean deviation is minimum if the deviations are taken from the median. So, it is less than that measured from any other value.

A series drawback of the mean deviation is that it cannot be used in statistical inference.

The difference between the maximum and the minimum obervations in data is called the ____________.

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

  1. mean of the data

  2. range of the data

  3. mode of the data

  4. median of the data

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Correct Option: B
Explanation:

In arithmetic, the range of a set of data is the difference between the largest and smallest values.

So, difference between minimum and maximum values is called range.

For the measure of centre tendency, which the following is not true.

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

  1. $Z=3M-2\bar{x}$

  2. $2\bar{x}+Z=3M$

  3. $2\bar{x}-3M=-Z$

  4. $2\bar{x}=Z-3M$

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Correct Option: D
Explanation:

We have, $Z=3M-2\bar{x}$
$\therefore 2\bar{x}+Z=3M$
or $2\bar{x}-3M=-Z$

$2\bar{x}=-Z+3M$
$\therefore 2\bar{x}=Z-3M $ is not true

Range of data $7, 8, 2, 1, 3, 13, 18$ is?

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

  1. $10$

  2. $15$

  3. $17$

  4. None of the above

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Correct Option: C
Explanation:

$\begin{matrix} 7,8,2,1,3,13,18, \ range\, \, of\, \, data=\left( { \max  imum-\min  imum } \right)  \ =\left( { 18-1 } \right) =17\, \, \, \, \, Ans. \  \end{matrix}$