BUSINESS STATISTICS NOTESB.COM 2ND AND 3RD SEM NEW SYLLABUS (CBCS PATTERN) MEASURE OF DISPERSION
Definition of Dispersion
The rate of distribution given one data represents all data. But a single measure cannot adequately describe a set of observations, unless all the observations are the same. It is necessary to describe the variability or scattering of the guard. In two or more distributions the average value may be the same but there may still be significant differences in distribution structure. Dispersion rate helps to study this important distribution factor.
In the words of Brooks and Dick, ”Dispersion is the degree of dispersion or variability in average value.
With the words Simpson and Kafka, ”The rate of mass dispersion in a series about a scale is called the rate of variance or scattering.
It is clear from the discussion above that Dispersion is a measure of diversity. It measures the level at which objects differ from the center. Dispersion is also known as a second-degree scale. Distribution includes width, definition deviation, quartile deviation, and standard deviation. Mean, Median and Mode is the order of the 1 order.
Purpose and Significance of the Dispersion Rate
Dispersion measures are required for the following purposes:
(i) Determining the reliability of the measure. If the scattering is small, the medium may be unreliable and if the distribution is large data, the medium may not be possible.
(ii) Acting as the basis for managing diversity by determining the environment and cause of diversity.
(iii) To compare two or more series in their diversity. A high degree of diversity can mean little similarity and a low level of diversity will mean great similarities.
(iv) Facilitate the implementation of other mathematical measures such as correlation analysis, mathematical quality control, regression analysis etc.
Types of Dispersion Rates
The degree of dispersion can be broadly divided into two types: -
a. Complete measures of dispersion: Divided into
(i) Width
(ii) It means Deviation
(iii) General Deviation
(iv) Quartile Deviation
(v) Ijika Lorenz
b. Dispersion rates: Divided into
(i) Coefficient of Range
(ii) Coefficient of Mean Deviation
(iii) Coefficient of Variation
(iv) Coefficient of Quartile Deviation.
Differences between total and related scatter rate:
1. Complete measures depend on the unit of assumptions considered while the corresponding scatter rates do not have units.
2. In order to compare two or more distributions, it is considered limited estimates and not complete scattering measures.
3. Compared to complete scatter measures, scatter rates are difficult to calculate and understand.
Desirable structures for good dispersion rate (Variation)
The following are the key factors that should satisfy a good dispersal rate:
1. It should be easy to understand and easy to calculate.
2. It should be easy to calculate.
3. It should be based on all things.
4. Excessive prices should not be affected.
5. It should be strongly defined.
6. Must be able to continue treatment for algebra.
7. Must have sample stability.
Description of Distance | Competence and Comprehensive Qualities
Width: Width is defined as the difference between the value of the smallest object and the value of the largest object included in the distribution. It is an easy way to measure dispersion. Figuratively,
Range = Maximum value (L) - Minimum value (S)
The relative correlation coefficient, called the coefficient of width, is obtained using the following formula: Coefficient of Range = (L- S) / (L + S)
Grade Qualification:
(i) It is easy to understand and easy to calculate.
(ii) It takes less time.
Demerits of Range:
(i) It is not based on each distribution item.
(ii) Most affected by excessive values.
(iii) The scope value is strongly influenced by the variability of the samples
(iv) Scope cannot be calculated in the event of an open distribution.
Significance of Quartile Divergence (Q.D) OR Quarterly Divergence | Advantages and disadvantages of QD
QD is part of the difference between the upper and lower quartiles. Figuratively, QD = ½ (Q3- Q1).
QD is a complete measure of dispersion. The QD correlation coefficient, called the QD coefficient, is obtained using the following formula: Coefficient of QD = (Q3 - Q1) / (Q3 + Q1). The QD Coefficient can be used to compare the degree of variability in different distributions.
QD Benefits:
(i) Based on 50% recognition.
(ii) Excess rates are not affected.
(iii) In the case of open distribution, it may be calculated.
QD Benefits:
(i) It is not based on each distribution item.
(ii) Unable to perform alternative algebraic treatments.
(iii) The scope value is significantly affected by the variability of the samples
Definition of Meaning Deviation (M.D) | Advantages and disadvantages of MD
M.D: With a particular set of observations, MD is defined as the arithmetic definition of the total deviation of the observed from the correct measurement of the medial inclination. The computer formula for MD says:
MD = ∑│D│ / N
MD is a complete measure of dispersion. The associated correlation coefficient of MD, called the coefficient of MD, is obtained by dividing the standard deviation by a certain scale used to calculate the mean deviation. Therefore, if MD is calculated from the limits, the coefficient of deviation from the definition will be b