Measures of Dispersion Test

Result

Measures of Dispersion Test - 4

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Question 1
1 / -0

What would happen to the variance of a data set if we multiplied every observation by 5?

A
Variance decreased by 25

B
Variance increased by 25

C
Variance decreased by 25

D
Variance increased by 55

Solution

Change in variance is the square of change in scale.
Question 2
1 / -0

While drawing Lorenz curve zero of X-axis and 100 on Y-axis are joined by a line. This line is known as

A
Line of unemployment

B
Line of equal distributions

C
Line of cumulative percentage of total national income

D
None

Solution

A perfectly equal income distribution would be one in which every person has the same income. In this case, the bottom N% of society would always have N% of the income. This can be depicted by the straight line y = x; called the "line of perfect equality."
Question 3
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The _______________ is the easiest measure of dispersion to calculate.

A
Mean absolute deviation

B
Range

C
Standard Deviation

D
Variance

Solution

It is easy to calculate because of a simple formula R= L-S where L is largest observation and S is smallest observation.
Question 4
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Which information is false regarding Lorenz curve

A
The Area between the line of equal distribution and the plotted curve gives the extent of inequality in the items. The larger the area, more is the inequality

B
The Lorenz curve devised by Dr. Max O. Lorenz is a graphic method of studying dispersion.

C
Used this technique to show employment of a group of people

D
The Lorenz curve always lies below the line of equal distribution, unless the distribution is uniform

Solution

The Lorenz curve, developed by Max O Lorenz in 1905, is a graphical representation of the distribution of the income or of wealth. It is used to represent inquality of the wealth distribution.
Question 5
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In case of open-ended classes, an appropriate measure of dispersion to be used is

A
Quartile Deviation

B
Range

C
Standard Deviation

D
Variance

Solution

As it is not much affected by extreme situations.
Question 6
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When should measures of location and dispersion be computed from grouped data rather than from individual data values?

A
Whenever computer packages for descriptive statistics are unavailable

B
Only when individual data values are unavailable

C
As much as possible since computations are easier

D
Only when the data are from a population

Solution

A fundamental task in many statistical analyses is to estimate a location parameter for the distribution; i.e., to find a typical or central value that best describes the data. Measures of location describe the central tendency of the data. They include the mean, median and mode. A measure of dispersion quantifies how much persons in the group vary from each other and from our measure of central location. Measures of dispersion describe the spread of the data. They include the range, interquartile range, standard deviation and variance.
Question 7
1 / -0

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is

A
Inter quartile range

B
Standard Deviation

C
The absolute value of the range

D
Range

Solution

Standard deviation for a given set of observations is defined as root mean square deviation when deviations are taken from mean.
Question 8
1 / -0

The numerical value of the standard deviation can never be

A
Negative

B
Larger than the variance

C
Zero

D
None

Solution

As it is calculated from sum of squared deviations which can never be negative.
Question 9
1 / -0

The variance can never be

A
larger than the standard deviation

B
Smaller than the standard deviation

C
Negative

D
Zero

Solution

It is a square of standard deviation and square of anything is non negative.

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Re-Attempt Weekly Quiz Competition

Measures of Dispersion Test - 4

Result

Measures of Dispersion Test - 4

Score

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Rank

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SHARING IS CARING

Question 1

Variance decreased by 25

Variance increased by 25

Variance decreased by 25

Variance increased by 55

Solution

Question 2

Line of unemployment

Line of equal distributions

Line of cumulative percentage of total national income

None

Solution

Question 3

Mean absolute deviation

Range

Standard Deviation

Variance

Solution

Question 4

The Area between the line of equal distribution and the plotted curve gives the extent of inequality in the items. The larger the area, more is the inequality

The Lorenz curve devised by Dr. Max O. Lorenz is a graphic method of studying dispersion.

Used this technique to show employment of a group of people

The Lorenz curve always lies below the line of equal distribution, unless the distribution is uniform

Solution

Question 5

Quartile Deviation

Range

Standard Deviation

Variance

Solution

Question 6

Whenever computer packages for descriptive statistics are unavailable

Only when individual data values are unavailable

As much as possible since computations are easier

Only when the data are from a population

Solution

Question 7

Inter quartile range

Standard Deviation

The absolute value of the range

Range

Solution

Question 8

Negative

Larger than the variance

Zero

None

Solution

Question 9

larger than the standard deviation

Smaller than the standard deviation

Negative

Zero

Solution

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