DISPERSION OF VARIABLE IN RESEARCH ANALYSIS

DISPERSION OF
VARIABLE
SUBMITTED TO RESPECTED:-
Mr. DHARMENDRA KUMAR HARDENIYA
LECTURER OF STATISTIC
SCPM COLLEGE OF NURSING AND
PARAMEDICAL COLLEGE

SUBMITTED BY
Ms. Khushboo singh
M.SC Nursing Ist year

Definition of Dispersion
• Dispersion measures the variability of a set of
observations among themselves or about
some central values
• The measurement of the scatterness of the
mass of figure in a series about an average is
called measure of variation or dispersion

Purposes of Dispersion
• To determine the reliability of average;
• To serve as a basis for the control of the
variability
• To compare to or more series with regard to
their variability and
• To facilitate the computation of other
statistical measures.

Properties of a Good Measures of
Dispersion
• It should be simple to understand.
• It is should be easy to compute.
• It is should rigidly defined.
• It should be based on all observations.
• It should have sampling fluctuation.
• It should be suitable for further algebraic
treatment.
• It should be not be affected by extreme
observations.

Measures of Dispersion
There are two kinds of Measures of Dispersion:
• 1. Absolute measures of dispersion
• 2. Relative measures of dispersion

Range
• Range is the difference between the largest &
smallest observation in set of data.
• In symbols, Range = L – S.
Where, L = Largest value.
S = Smallest value.
• In individual observations and discrete series,
L and S are easily identified.

Coefficient of Range
The percentage ratio of range & sum of
maximum & minimum observation is known
as Coefficient of Range.
• Coefficient of Range =Xmax – Xmin×100
Xmax+ X𝑚𝑖𝑛

EXAMPLE
• The monthly incomes in taka of seven
employees of a firm are 5500,5750,6500,67
50,7000 & 8500. Compute Range & Coefficient
of Range.
Solution
• The range of the income of the employees is
Range = 8500-5500
= TK 3000

EXAMPLE
• Coefficient of Range =Xmax – Xmin
Xmax+ Xmin×100
=8500−5500
8500+5500× 100
=3000
14000× 100
= 21.43%

Merits
1. The range measure the total spread in the set of
data.
2. It is rigidly defined.
3. It is the simplest measure of dispersion.
4. It is easiest to compute.
5. It takes the minimum time to compute.
6. It is based on only maximum and minimum values

Demerits
1. It is not based on all the observations of a set
of data.
2. It is affected by sampling fluctuation.
3. It is cannot be computed in case of open-end
distribution.
4. It is highly affected by extreme values

When To Use the Range
• The range is used when you have ordinal data
or you are presenting your results to people
with little or no knowledge of statistics.
The range is rarely used in scientific work as it
is fairly insensitive.
• It depends on only two scores in the set of
data, XL and XS Two very different sets of data
can have the same range:1 1 1 1 9 vs 1 3 5 7 9

Quartile Deviation
• • The average difference of 3rd & 1st Quartile
is known as Quartile Deviation.
• Quartile Deviation =Q3−Q1
2

Coefficient of Quartile Deviation
• The relative measure corresponding to this
measure, called the coefficient of quartile
deviation, is defied by
• Coefficient of Quartile Deviation=
• 𝑥 = 3_ 1
𝑄 𝑄
𝑄3+ 1 100
𝑄 ∗

Advantage of Quartile Deviation
• It is superior to range as a measure of
variation.
• It is useful in case of open-end distribution.
• It is not affected by the presence of extreme
values.
• It is useful in case of highly skewed
distribution.

Disadvantage of Quartile Deviation
• It is not based on all observations.
It ignores the first 25% and last 25% of the
observation.
• It is not capable of mathematical manipulation.
• It is very much affected by sampling fluctuation.
• It is not a good measure of dispersion since it
depends on two position measure.

Mean Deviation
• The difference of mean from their observation
& their mean is known as mean deviation

Mean Deviation for ungrouped data
• Suppose X1, X2,……….,Xn are n values of
variable, and is the mean and the mean
deviation (M.D.) about mean is defined by

Mean Deviation for grouped data

Coefficient of Mean Deviation
• The Percentage ratio of mean deviation &
mean is as known as Coefficient of Mean
Deviation(C.M.D.).

For Grouped & Ungrouped Data C.M.D.

Merits of Mean Deviation:
• 1. It is easy to understand and to compute.
• 2. It is less affected by the extreme values.
• 3. It is based on all observations.
Limitations of Mean Deviation:
• 1. This method may not give us accurate results.
• 2. It is not capable of further algebraic treatment.
• 3. It is rarely used in sociological and business
studies

Variance
• The square deviation of mean from their
observation and their mean is as known as
variance.

DISPERSION OF VARIABLE IN RESEARCH ANALYSIS

Standard Deviation
• The square deviation of mean from their
observation & the square root variance is as
known as Standard Deviation

Merits of Standard Deviation
1. It is rigidly defied.
2. It is based on all observations of the
distribution.
3. It is amenable to algebraic treatment.
4. It is less affected by the sampling fluctuation.
5. It is possible to calculate the combined
standard deviation

Demerits of Standard Deviation
• As compared to other measures it is difficult
to compute.
• It is affected by the extreme values.
• It is not useful to compare two sets of data
when the observations are measured in
different ways

Coefficient of Variation
• • The percentage ratio of Standard deviation
and mean is as known as coefficient of
variation

EXAMPLE
• Consider the measurement on yield and plant height of a
paddy variety. The mean and standard deviation for yield
are 50 kg and10 kg respectively. The mean and standard
deviation for plant height are 55 am and 5 cm respectively.
• Here the measurements for yield and plant height are in
different units. Hence the variabilities can be compared
only by using coefficient of variation.
• For yield, CV=10
50 × 100
= 20%

Conclusion
 The measures of variations are useful for further treatment
of the Data collected during the study.
The study of Measures of Dispersion can serve as the
foundation for comparison between two or more frequency
distributions.
 Standard deviation or variance is never negative.
When all observations are equal, standard deviation is zero.
when all observations in the data are increased or
decreased by constant, standard deviation remains the
same.

DISPERSION OF VARIABLE IN RESEARCH ANALYSIS

More Related Content

Similar to DISPERSION OF VARIABLE IN RESEARCH ANALYSIS (20)

More from khushboo singh (14)

Recently uploaded (20)

DISPERSION OF VARIABLE IN RESEARCH ANALYSIS