Agriculture Reference
In-Depth Information
, the approximate median value
can also be worked out from the intersection
point of the two cumulative frequency (less
than and more than that type) curves.
Alternatively
preceding the 50th percentile class,
f
p
50
is the
frequency of the 50th percentile class, and CI is
the width of the 40th percentile class.
8
N=
10
F
d
8
1
f
d
8
8th decile or
D
8
¼ x
l
þ
:
CI
Properties of Median:
1. Median is easy to calculate and understand.
2. For its calculation, it does not require to have
all observations.
3. For qualitative data also, median can be
worked out.
4. Median cannot be put under mathematical
treatments like AM and GM.
5. Arrangements of data are necessary for the
calculation of median.
where
x
l
is the lower class boundary of the 8th
decile class,
N
F
d
8
1
is the cumula-
tive frequency (less than the type) of the class
preceding the 8th decile class,
is the total frequency,
f
d
8
is the frequency
of the 8th decile class, and CI is the width of the
8th decile class.
N=
F
q
3
1
f
q
3
3
4
Uses of Median:
Median is a useful measure for
both quantitative and qualitative characters.
Using the measure in agriculture, socioeconomic
and other field researchers divide the whole pop-
ulation into parts for any subsequent action-
oriented research program.
3rd quartile or
Q
3
¼ x
l
þ
:
CI
where
x
l
is the lower boundary of the 3rd quartile
class,
n
Fq
3
1
is the cumula-
tive frequency, (less than the type) of the class
preceding the 3rd quartile class,
is the total frequency,
Percentiles, Deciles, and Quartiles (Partition
Values):
By modifying the formula for median, different
percentiles/deciles/quartiles can very well be
worked out to divide the whole population into
as many groups as one would like to have. Just
by substituting
f
q
3
is the fre-
quency of the 3rd quartile class, and CI is the
width of the 3rd quartile class.
Example 8.13.
Q
3
values of
yield (q/ha) from the following frequency table.
Find the
P
50
,
D
8
,and
N
/2 in the median formula by
“
/4” and the corres-
ponding cumulative frequencies (less than the
type), where “
Np
/100,” “
Nd
/10,” or “
Nq
Yield
classes
Frequency
(
f
i
)
Mid
value (
x
i
)
Cumulative
frequency (CF
<
)
10-20
16
15
16
th
percentile,
d
th decile, and
q
th quartile, respec-
tively, one can get different percentile/decile/
quartile values.
Thus, the formula for some percentiles,
deciles, or quartiles is as follows:
p
,” “
d
,” and “
q
” denote the
p
20-30
54
25
70
30-40
14
35
84
40-50
11
45
95
50-60
10
55
105
60-70
10
65
115
70-80
8
75
123
80-90
7
85
130
P
50
50
N=
100
F
p
50
1
f
p
50
50th percentile or
P
50
¼ x
l
þ
:
CI
N=
F
p
50
1
f
p
50
50
100
¼ x
l
þ
:
CI
¼
Median
50
:
130
=
100
16
¼
20
þ
10
¼
29
:
074
54
8
N=
10
F
d
8
1
f
d
8
where
x
l
is the lower class boundary of the 40th
percentile class,
N
D
8
¼ x
l
þ
:
CI
8
130
=
10
95
F
p
50
1
is the cumula-
tive frequency (less than the type) of the class
is the total frequency,
¼
50
þ
10
¼
59
10
