Agriculture Reference
In-Depth Information
of the data reveals that in society 1, the innovation
remains in between 14 and 19; on the other hand,
in society 2 it remains between 9 and 24.5. Thus,
the innovation indices are more dispersed in soci-
ety 2 than in society 1, in spite of having the same
average performance for both the societies. Thus,
from the above results, two conclusions can be
drawn: (a) the maximum innovation potentiality
and innovation variability of society 1 is less than
in society 2 and (b) given a better attention, people
in society 2 can be better innovative by attaining
its full potentiality.
dispersions are available in the theory of statistics.
Before going into the details on the discussion of
the different measures of dispersion, let us try to
examine the characteristics of a good measure of
dispersion. There should not be any ambiguity in
defining a measure; it should be clear and rigid in
definition. Unless a measure is convincing, that is,
easily understood and applicable by the user, it is
of least importance. For further application of a
measure, it should be put easily under mathemati-
cal treatments. In order to reflect the true nature of
the data, a good measure should try to take care of
all the observations, and it should lay equal impor-
tance to each and every observation without being
affected by the extreme values.
Measures of Dispersion
:Likethemeasuresof
central tendency, there is a need to have measures
for dispersion also. In fact, different measures of
Measures of dispersion
Absolute measure
Relative measures
a) Range
b) Mean deviation
c) Quartile deviation
d) Standard deviation
e) Moments
a) Coefficient of quartile deviation
b) Coefficient mean deviation
c) Coefficient of variation
8.2.2.1 Absolute Measures of Dispersion
The absolute measures of dispersion have the
units according to those of variables, but relative
measures are pure number; as such are
2. Though range is not based on all the
observations, it cannot be worked out if
there are missing values.
3. Range is very much affected by sampling
fluctuations.
In spite of all these drawbacks, range is
being used in many occasions only because
of its simplicity and of having a first-hand
information on the variation of the data.
unit-free
measures. Thus, unit-free measures can be used
to compare distributions of different variables
measured in different units.
(a)
Range
: A range of a set of observations is the
difference between the maximum value and
the minimum value of a set of data. Thus,
Rx ¼ X
max
-
Mean Deviation
(b)
: The mean deviation of var-
”
for a given set of observations. In the above
example, the ranges for two societies are
19
14
¼
5 and 24.5
9
¼
15.5,
X
min
is the range of variable “
X
iable “
X
”(
x
1
,
x
2
,
x
3,
,
x
n
) about any arbi-
trary point “
” is defined as the mean of the
absolute deviation of the different values of
the variable from the arbitrary point “
A
” and
A
respec-
P
n
tively, for society 1 and society 2.
Uses of Range
P
n
i¼
1
n
1
is denoted as MD
A
¼
1
X
i
A
,
1
f
i
: Range can be used in any
type of continuous or discrete variables.
Range has its uses in the field of stock market
(daily variation), in meteorological forecast-
ing, in statistical quality control, etc.
Advantages and Disadvantages of Range:
1. Range is rigidly defined and can be calcu-
lated easily.
i¼
P
i¼
1
f
i
X
i
A
for grouped data.
Similarly, instead of taking the deviation
from the arbitrary point “
A
,” one can take the
deviation from the arithmetic mean, median,
or mode also. Actually, the mean deviation of
variable “
j
j
” is defined as the mean of the
absolute deviation of different values of the
X
