Agriculture Reference
In-Depth Information
Properties of Mode:
(a) Mode is easy to calculate and understand.
(b) For its calculation, it does not require to have
all observations.
(c) Mode cannot be put under mathematical
treatments like AM and GM.
(d) It is least affected by the presence of extreme
values.
(e) A distribution may have one or more (when
two or more values have same frequency)
modes. If a distribution has more than two
modes,
observations. Among the three means, the AM
GM
HM, the AM suffers from extreme value
while the GM is suitable for data which changes
in definite ratio or rate. Thus, the nature of data
and the objective of the study along with the
characteristics of the measures are the major
point of consideration during the selection of
appropriate measure of central tendency.
8.2.2 Measures of Dispersion,
Skewness, and Kurtosis
it
is
said to be a multimodal
distribution.
Uses of Mode
: Mode is of little use unless the
number of observations is very high. Mode can
best be used in case of qualitative characters like
a race of people, awareness pattern of people of
certain locality, and types of crop or cropping
pattern grown in a particular locality.
The essence of analysis of research data is to
unearth the otherwise hidden truth from a set of
data. In this direction, if the measures of central
tendency be the search for a value around which
the observations have the tendency to center
around, then dispersion is a search for a spread
of the observations within a given data set. Thus,
if central tendency is the thesis, then dispersion is
the antithesis. The tendency of the observations
of any variable to remain scattered/dispersed
from a central value or any other value is
known as dispersion of the variable. A researcher
must have good knowledge about the central
tendency and the dispersion of the research data
he/she is handling to discover the truth that had
remained hidden so long. This is more essential
because neither the measure of central tendency
nor the measure of dispersion in isolation can
reveal the nature of the information.
Let us take the following example:
8.2.1.4 Midpoint Range
Midpoint range is simply the arithmetic mean of
the lowest and highest value of a given set of
data. If
are the lowest and highest values
of a given set of data, respectively, the midpoint
range (MD
L
and
U
)/2. As such, it is devoid of
the many good properties of average mentioned
in this section for different averages. It takes care
of only the two extreme values and as such
affected by these values. Even then it can provide
some sort of information about the data.
r
)is(
L
+
U
Selection of Proper Measure of Central Tendency
:
All the measures of central tendency cannot be
used everywhere. The selection of appropriate
measure should be based on merits and demerits
of the measures of central tendency. Qualitative
data can be measured through median and mode,
but these two measures are not based on all
Example 8.16.
To measure the innovation index,
ten persons from each of the society were stud-
ied, and the following table gives the indices
individually.
Innovation index
Society 1
15.00
16.50
16.00
18.00
17.00
18.50
19.00
18.50
17.50
14.00
Society 2
10.50
21.50
22.50
9.00
24.50
11.50
23.00
20.00
17.00
10.50
From the above, one can have the arithmetic
means,
the central tendency measured in terms of arith-
metic mean for innovation index for the above
two societies is same. But a critical examination
X
1
¼
¼
(15 + 16.5 +
+ 14)/10
7and
X
2
¼
(10.50 + 21.50 +
+10.50)/10
¼
17. Thus,
