Measures of Dispersion Test

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Measures of Dispersion Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

The co-efficient of mean deviation of first five natural numbers is _____.

A
$$0.75$$

B
$$0.4$$

C
$$0.5$$

D
$$0.7$$

Solution

The first five natural numbers are 1,2,3,4,5
Mean = 3
Mean deviation = 6/5 = 1.2
Coefficient of mean deviation is calculated by dividing the mean deviation of the series by its corresponding average.
Coefficient of mean deviation = Mean deviation / mean
= 1.2 /3
= 0.4
Question 2
1 / -0

Which measure of dispersion has a different unit other than the unit of measurement of values?

A
Range

B
Mean deviation

C
Standard deviation

D
Variance

Solution

Variance is the mean of the squares of the deviations from the mean. Variance is the square of standard deviation. Therefore any unit of a given set is converted into squares at the time of calculating the variance.
Question 3
1 / -0

A set of values is said to be relatively uniform if it has ________.

A
high dispersion

B
zero dispersion

C
little dispersion

D
negative dispersion

Solution

A set of values from an observation is said to be relatively uniform if all the observations of the series have very little dispersion from each other.
Question 4
1 / -0

If the minimum value in a set is $$15$$ and its range is $$55$$, the maximum value of the set is _______.

A
$$40$$

B
$$60$$

C
$$80$$

D
$$70$$

Solution

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 = 55

In the given series, H= x and L= 15

Range => x-15 = 55
=> x = 55+15 = 70
Question 5
1 / -0

If the value of a set are measured in kgs, the unit of variance will be ______.

A
$$Kg^2$$

B
Kg

C
$$Kg^3$$

D
No unit

Solution

Variance is the mean of the squares of the deviations from the mean. Variance is the square of standard deviation. Therefore any unit of a given set is converted into squares at the time of calculating the variance.
Question 6
1 / -0

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

A
Range

B
Mean deviation

C
Standard deviation

D
None of the above

Solution

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.
Question 7
1 / -0

In distribution $$25\%$$ of the observations are less than $$46$$ and $$25\%$$ of the observations are more than $$54$$. The quartile deviation of the distribution is _______.

A
$$3$$

B
$$7$$

C
$$4$$

D
$$6$$

Solution

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q₁ and the third quartile is denoted as Q₃ .

Q₁= 46 and Q₃=54

Quartile deviation = (Q₃-Q₁) /2

                             = (54-46)/2

                             = 8/2

                             = 4
Question 8
1 / -0

Which measure of dispersion ensures lowest degree of reliability?

A
Range

B
Mean deviation

C
Quartile deviation

D
Standard deviation

Solution

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most affected measures of dispersion by the extreme values of the series therefore it has the lowest degree of reliability.
Question 9
1 / -0

The sum of $$10$$ observations is $$110$$ and the sum of squares of observations is $$2900$$, their standard deviation is ______.

A
$$13$$

B
$$8$$

C
$$10$$

D
$$9$$

Solution

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Standard deviation = { (sum of the squares of the observations/ number of observations ) – (sum of observations/ number of observations ) } ^½

= { (2800/10) –(110/10) } ^½

= { 280- 11}^1/2

= (169) ^½

= 13
Question 10
1 / -0

The C.V of a distribution is $$80\%$$ and the mean of the distribution is $$40$$, the S.D of the distribution is ________.

A
$$33$$

B
$$32$$

C
$$35$$

D
$$0.30$$

Solution

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.
Coefficient of variation = ( standard deviation / mean )
=> 80 /100 = S.D / 40
=> S.D = 32

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Measures of Dispersion Test - 33

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Measures of Dispersion Test - 33

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Question 1

$$0.75$$

$$0.4$$

$$0.5$$

$$0.7$$

Solution

Question 2

Range

Mean deviation

Standard deviation

Variance

Solution

Question 3

high dispersion

zero dispersion

little dispersion

negative dispersion

Solution

Question 4

$$40$$

$$60$$

$$80$$

$$70$$

Solution

Question 5

$$Kg^2$$

Kg

$$Kg^3$$

No unit

Solution

Question 6

Range

Mean deviation

Standard deviation

None of the above

Solution

Question 7

$$3$$

$$7$$

$$4$$

$$6$$

Solution

Question 8

Range

Mean deviation

Quartile deviation

Standard deviation

Solution

Question 9

$$13$$

$$8$$

$$10$$

$$9$$

Solution

Question 10

$$33$$

$$32$$

$$35$$

$$0.30$$

Solution

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