Agriculture Reference
In-Depth Information
the maximum and minimum values of
variable “ X .”
measures of central tendency as well as measure
of dispersion but
they differ widely in their
2.
Coefficient of dispersion based on quartile
nature.
Q 3 Q 1
2
Q 3 þQ 1
2 ¼ Q 3 Q 1
deviation
: It is defined as
Q 3 þQ 1
Example 8.20.
Given below are the two fre-
quency distributions for a number of nuts per
bunch with respective means as 12.62 and 12.11
and standard deviations as 3.77 and 3.484, respec-
tively. Thus, both the distributions have almost the
same measure of central tendency as well as mea-
sure of dispersion. But a close look at the graphs
drawn for the two frequency distributions shows
that they differ widely in nature (Fig. 8.12 ).
Along with the measures of dispersion and
central tendency, there should be certain
measures which can provide the exact picture of
the given data set.
Coefficient of dispersion based on mean
deviation from mean / median / mode / arbi-
trary point
3.
: This measure is given by
MD mean
=
median
=
mode etc
:
Mean = Median = Mode
4.
Coefficient of dispersion based on standard
deviation
: It is defined as σ X
X
, where
σ X
and
X
are the standard deviation and arithmetic
mean of variable “
,” respectively. The
more widely used and customary coefficient
of dispersion based on standard deviation is
the “
X
σ X
coefficient of variation (CV)
X
100
:
talk
about the nature of the frequency distribution.
The s
Skewness
and
kurtosis
8.2.2.3 Skewness and Kurtosis
Neither the measure of central tendency nor the
measure of dispersion alone is sufficient to
extract the inherent characteristics of a given set
of data. We need to combine both these measures
together. We can come across with a situation
where two frequency distributions have the same
of a frequency distribution is
the departure of the frequency distribution from
symmetricity.
A frequency distribution is either
kewness
symmetric
or
. Again an asymmetric/
skewed distribution may be
asymmetric/skewed
positively skewed
or
negatively skewed
.
Frequency distribution
Symmetric
Asymmetric / Skewed
Positively skewed
Negatively skewed
Example 8.21.
Let us take the example of the
panicle length in three different varieties of
paddy. The frequency distributions and the
corresponding graphical
refers to the peakedness of a frequency
distribution. While skewness refers to the horizon-
tal property of the frequency distribution, kurtosis
refers to the vertical nature of the frequency distri-
bution. According to the nature of peak, a distribu-
tion is
Kurtosis
representations
are
given in Figs. 8.13 , 8.14 , and 8.15 .
Among the different measures, the measures
based on moments are mostly used and are given
as
in
nature. Kurtosis is measured in terms of β 2 ¼ m 4
m
leptokurtic
,
mesokurtic
, or
platykurtic
,
p 1 ¼ γ 1 ¼ m 3
2
2
p
m
where
m 2 are the 4th and 2nd central
moments, respectively. If
m 4 and
m 2 are the 3rd
and 2nd central moments, respectively. It may be
noted that all the measures of skewness have no
units; these are pure numbers and equal to zero
when the distribution is symmetric. Further, it is
to be noted that
, where
m 3 and
3
2
β 2 >
3,
β 2 ¼
3, the distri-
bution ismesokurtic, and if
3, the distribution
is platykurtic. In the case of a normal distribution
mentionedinChap. 6 , if this is taken as standard,
the quantity
β 2 <
3 measures the what is known
as excess of kurtosis. If
β 2
0. The sign of
p 1
2
3
m
m
β 1 ¼
2
β 2 >
3, the distribution
3
is leptokurtic, and
β 2 ¼
3,
the distribution is
depends on the sign of
m 3 .
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