Measures of Dispersion Test

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Measures of Dispersion Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is true of a measure of dispersion?

A
Mean deviation does not follow algebraic value

B
Range is crudest measure

C
Coefficient of variation is a relative measure

D
All the above statements
Solution
- Mean deviation is the arithmetic average of the deviations of the observed values from an average of the observed values. Since Mean deviation do not include negative value of the deviations. Therefore, it does not follow the algebraic value of the deviations.
- 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. Since it is the most affected measures of dispersion by the extreme values of the series, it is regarded as the crudest measure.
- Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion.
Question 2
1 / -0

The relation between variance and standard deviation is ________.

A
variance is the square root of standard Deviation

B
square of the standard deviation is equal to Variance

C
variance is equal to standard deviation

D
standard deviation is the square of the variance

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.

Variance is the mean of the squares of the deviations from the mean.

Standard deviation is the square root of variance or variance is the square of standard deviation.

S.D = {Var(X)}^1/2

or

Var(X) = (S.D)²
Question 3
1 / -0

Probability can take values from ______.

A
-3 to 3

B
-3 to 1

C
0 to 1

D
-1 to 1

Solution

Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1.
Question 4
1 / -0

Probability is expressed as _______.

A
percentage

B
ratio

C
proportion

D
all (a), (b), (c)

Solution

Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1.
Question 5
1 / -0

If A and B are events, the probability of occurrence of A and B simultaneously is given as _______.

A
P(A) + P(B)

B
$P(A\cup{B})$

C
P(AB)

D
P(A) P(B)

Solution

If A and B are two events, then P(AB) refers to as the probability of the occurrence of A and B simultaneously.
P(AB) = P(A) x P(B)
Question 6
1 / -0

Classical probability is measured in terms of _________.

A
absolute value and ratio both

B
a ratio

C
an absolute value

D
none of the above

Solution

Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Classical probability is usually expressed in terms of ratio as it measures the relation of the variables in their absolute form.
Question 7
1 / -0

If A and B are two events, the probability of occurrence of either A or B is given as _______.

A
P(A) + P(B)

B
$P(A\cup{B})$

C
P(A)P(B)

D
P(AB)

Solution

If A and B are two events, then A union B refers to the occurrence of either A or B or both which means all the elements of the two events have equal likely chances to occur in an event known as A union B.
Question 8
1 / -0

If each value of a series is multiplied by a constant, the coefficient of variation as compared to original value is _______.

A
increased

B
unaltered

C
decreased

D
zero

Solution

Variance is the mean of the squares of the deviations from the mean. Variance is not affected by the addition, subtraction, multiplication and division of the given value. Therefore, if each value of the series is multiplied by 15, the coefficient of variation will be unaltered.
Question 9
1 / -0

The coefficient of variation is?

A
The same as the variance

B
A measure of central tendency

C
A measure of absolute variability

D
A measure of relative variability

Solution

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.

Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion.
Question 10
1 / -0

The lorenz curve shows the relationship between_____________.

A
asset creation and income generation.

B
population groups and their respective income shares.

C
unemployment and inflation.

D
wages, labor hours and leisure.

Solution

Lorenz curve is the graphical representation that shows the relationship between the different population groups of the world with their respective income share assuming that income is unevenly distributed.

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Re-Attempt Weekly Quiz Competition

Measures of Dispersion Test - 35

Result

Measures of Dispersion Test - 35

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SHARING IS CARING

Question 1

Mean deviation does not follow algebraic value

Range is crudest measure

Coefficient of variation is a relative measure

All the above statements

Solution

Question 2

variance is the square root of standard Deviation

square of the standard deviation is equal to Variance

variance is equal to standard deviation

standard deviation is the square of the variance

Solution

Question 3

-3 to 3

-3 to 1

0 to 1

-1 to 1

Solution

Question 4

percentage

ratio

proportion

all (a), (b), (c)

Solution

Question 5

P(A) + P(B)

P(A∪B)P(A\cup{B})P(A∪B)

P(AB)

P(A) P(B)

Solution

Question 6

absolute value and ratio both

a ratio

an absolute value

none of the above

Solution

Question 7

P(A) + P(B)

P(A∪B)P(A\cup{B})P(A∪B)

P(A)P(B)

P(AB)

Solution

Question 8

increased

unaltered

decreased

zero

Solution

Question 9

The same as the variance

A measure of central tendency

A measure of absolute variability

A measure of relative variability

Solution

Question 10

asset creation and income generation.

population groups and their respective income shares.

unemployment and inflation.

wages, labor hours and leisure.

Solution

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$P(A\cup{B})$

$P(A\cup{B})$