Agriculture Reference
In-Depth Information
Steps in Calculating the Mode:
1. Identify the modal class, that is, the class
having the maximum observation from the
frequency column.
2. Identify the lower class boundary (
3
N=
4
F
q
3
1
f
q
3
Q
3
¼ x
l
þ
:
CI
3
130
=
4
95
¼
50
þ
10
¼
52
:
5
10
x
l
), the
class width (CI), and the frequency (
Thus, from the above results, one can find that
50% (
f
mo
)
P
50
) plants have 29.074 q/ha or less yield,
75% (
values of the modal class.
3. Identify the frequency of the class preceding
the modal class (
Q
3
) plants have 52.5 q/ha or less yield,
and 80% (
D
8
) plants 59 q/ha or less yield.
f
m
1
) and also the frequency
of the class following the modal class (
f
m
+1
).
4. Use the above values in the formula for mode.
5. Mode will be having the same unit as that of
the variable.
8.2.1.3 Mode
The mode of a variable is defined as the value of
the observation having a maximum frequency.
Example 8.15.
Q
3
values
of yield (q/ha) from the following frequency
table.
Find the
P
50
,
D
8,
and
Example 8.14.
The number of accidents per day
on a specific road is given below:
15, 8, 7, 15, 10, 12, 13, 9, 10, 15, 8, 9, 10,
13,9,12, 10, 8, 10, and 7. Find the mode of the
number of accidents per day.
Yield
classes
Frequency
(
f
i
)
Mid value
(
x
i
)
Cumulative
frequency (CF
<
)
10-20
16
15
16
No. accidents per day 789 0 2 3 5
Frequency
20-30
54
25
70
2
3
3
5
2
2
3
30-40
14
35
84
40-50
11
45
95
50-60
10
55
105
From the above arrangement, it is found that
the maximum frequency is for the 10 accidents
per day. Hence, the mode is 10.
From a
60-70
10
65
115
70-80
8
75
123
80-90
7
85
130
grouped/classified frequency distribu-
tion
, the mode cannot be worked out as above.
The mode from a grouped frequency distribution
is calculated with the help of the following
formula:
1. The total number of observation is 130.
2. The modal class is 20-30.
3. The lower class boundary (
x
l
) is 20, the class
width (CI) is 10, and the frequency (
f
m
)is54
of the modal class.
4. The frequency of the class preceding the
modal class (
f
mo
f
mo
1
f
mo
f
mo
1
Mo
¼ x
l
þ
Þ
:
CI
;
ð
Þ þ f
mo
f
mo
þ
1
ð
f
m
1
) is 16 and the frequency
of the class following the modal class (
f
m
+1
)
where
x
l
is the lower class boundary of the modal
class,
f
me
1
is the frequency of the class preceding the
modal class,
f
mo
is frequency of the modal class,
f
me+1
is the frequency of the class following the
modal class, and
CI is the width of the modal class.
is 14.
So the mode of the above frequency distribu-
tion is
54
16
¼
þ
Þ
Mo
20
10
ð
54
16
Þþð
54
14
¼
24
:
87 q
=
ha
:
