Measures of Dispersion Test

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Measures of Dispersion Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

An ideal measure of dispersion is

A
Quartile deviation

B
The standard deviation

C
Range

D
The mean deviation

Solution

It posseses most of the features laid down for an ideal measure of dispersion.
Question 2
1 / -0

Lorenz Curve was devised by

A
Dr. Max B’Lorenz

B
Dr. Max O’Lorenz

C
Dr. Max D’Lorenz

D
Dr. Max A’Lorenz

Solution

It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.
Question 3
1 / -0

Lorenz Curve : Used this technique to show

A
equality of wealth and income of a group of people

B
inequality of wealth and income of a group of people

C
unemployment of a group of people

D
employment of a group of people

Solution

The Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O Lorenz in 1905 for representing inequality of the wealth distribution.
Question 4
1 / -0

Which of the following is false regarding Dispersion

A
Reveals how items are spread out on either side of the centre

B
Indicates high or low uniformity of the items

C
Difference or variation among the values

D
It serve to locate the distribution

Solution

Dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. Dispersion is contrasted with location or central tendancy, and together they are the most used properties of distributions.

Question 5

1 / -0

Match the following

a. Quartile deviation	i. the square root of the arithmetic mean of the squares of deviation of its items from their arithmetic mean
b. Mean deviation	ii. half of difference of third quartile and first quartile
c. Standard deviation	iii. the arithmetic mean of the deviations

(iii)

(ii)

(i)

(i)

(iii)

(ii)

(ii)

(i)

(iii)

(ii)

(iii)

(i)

Solution

Quartile Deviation (QD) means the semi variation between the upper quartiles (Q3) and lower quartiles (Q1) in a distribution. The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. If the data points are further from the mean, there is higher deviation within the data set.

Question 6
1 / -0

Find the value of range for the following Data 7, 9, 6, 8, 11, 10, 4

A
9

B
8

C
7

D
5

Solution

R= L-S where L is largest value and S is smallest value

R= 11-4= 7
Question 7
1 / -0

Find the co-efficient of range for the following data. 7, 9, 6, 8, 11, 10, 4

A
0.4667

B
0.3245

C
0.2351

D
0.4766

Solution

This is a relative measure of dispersion and is based on the value of the range. It is also called range coefficient of dispersion.Co-efficient of range= L-S/L+S= 7/15= 0.4667

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Measures of Dispersion Test - 5

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Measures of Dispersion Test - 5

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Question 1

Quartile deviation

The standard deviation

Range

The mean deviation

Solution

Question 2

Dr. Max B’Lorenz

Dr. Max O’Lorenz

Dr. Max D’Lorenz

Dr. Max A’Lorenz

Solution

Question 3

equality of wealth and income of a group of people

inequality of wealth and income of a group of people

unemployment of a group of people

employment of a group of people

Solution

Question 4

Reveals how items are spread out on either side of the centre

Indicates high or low uniformity of the items

Difference or variation among the values

It serve to locate the distribution

Solution

Question 5

(iii) (ii) (i)

(i) (iii) (ii)

(ii) (i) (iii)

(ii) (iii) (i)

Solution

Question 6

9

8

7

5

Solution

Question 7

0.4667

0.3245

0.2351

0.4766

Solution

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(iii)

(ii)

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(i)

(iii)

(ii)

(ii)

(i)

(iii)

(ii)

(iii)

(i)