Tag: measures of dispersion and skewness

Questions Related to measures of dispersion and skewness

Value of each sample observation is decreased by $25$, the range of the sample observation will ____________.

  1. increase by $25$

  2. remain same

  3. decrease by $25$

  4. increase by $2$ times


Correct Option: B

The range from the following observations is 
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$

  1. $24$

  2. $20$

  3. $30$

  4. $42$


Correct Option: A
Explanation:

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion.

Range = H - L 
In the given series, H= 34 and L+ 10 
Range = 34-10 = 24.

From the following detail find out coefficient of Quartile Deviation.
$3=64,Q1=50$

  1. $12.11$%

  2. $12.28$%

  3. $13.50$%

  4. $12.08$%


Correct Option: B

The $Q _3$ for the following distribution is

X 2 3 4 5 6 7 8 9 10 11
Y 3 6 9 18 20 14 10 10 7 2


  1. $6$

  2. $5$

  3. $8$

  4. $9$


Correct Option: C

The $8th$ decile of the following observations is
$29, 18, 15, 30, 42, 35, 34, 28, 45, 34$

  1. $44.6$

  2. $40.6$

  3. $34.15$

  4. $38.15$


Correct Option: B

If we plot the more than type and less than type frequency distributions of the same set of date, their graph intersect at a point which is known as ______.

  1. median

  2. mode

  3. mean

  4. none of the above


Correct Option: A

Which of the following relations among the location parameters does not hold?

  1. $Q _2 = Median$

  2. $P _50 = Median$

  3. $D _5 = Median$

  4. $D _4 = Median$


Correct Option: D

In a group, $2$ students spend Rs$8$ daily, $3$ students spend Rs$10$ daily and $5$ students spend Rs$6$ daily. The average spending of all $10$ students is _______.

  1. $7.6$

  2. $5.8$

  3. $8.5$

  4. $6.7$


Correct Option: A

The $P _82$ for the following distribution is

X 2 3 4 5 6 7 8 9 10 11
Y 3 6 9 18 20 14 10 10 7 2


  1. $6$

  2. $5$

  3. $8$

  4. $9$


Correct Option: D

Which of the following measures of dispersion can attain a negative value?

  1. Range

  2. Mean deviation

  3. Standard deviation

  4. None of the above


Correct Option: D
Explanation:

Measure of dispersion is a statistical method to find a specific value from a dispersed series where the extent to which various values of the series tend to disperse from each other or from the average is measured. So all the measures of dispersion from range to standard deviation has positive value.