Mode is that value which occurs most
frequently in a statistical distribution.
According to A.M. Tuttle, “Mode is the value
which has the greatest frequency density in
its immediate neighborhood.”
A distribution can also have more than one
nodal value. A distribution having one nodal
value is known as Uni-Modal. A distribution
having two or more nodal values is known as
Bi-Nodal or Multi-Nodal respectively.
Relation
between
(Mean),
M (Median) and Z (Mode)
For a moderately asymmetric series
Individual Series:
-
Arrange the series in ascending or
descending order
-
Find the term which is occurring most of
the times. This term is Mode (Z).
To find the Mode in a series
Arranging the series in ascending order
In this series 10 is occurring 3 times so Z
= 10.
Discrete Series:
In discrete series the value which has
highest frequency is Mode.
To find the mode in a series
|
X: |
5 |
8 |
11 |
15 |
24 |
|
Frequency (f): |
3 |
8 |
13 |
20 |
12 |
In this series the highest frequency is 20
and the variable corresponding to this is 15
so the Mode = Z = 15
Continuous Series:
To calculate the Mode, we use the following
formula
Where L = Lower limit of Modal interval
f1 = frequency corresponding to
Modal interval
f2 = frequency of succeeding
Modal Interval
f0 = frequency of preceeding
Modal interval
i = Length of Modal interval
Mode can also be calculated by taking the
upper limit
Where L is the upper limit.
To calculate the Mode of a continuous series
|
X: |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
|
f: |
5 |
12 |
20 (f0) |
43 (f1) |
32 (f2) |
21 |
8 |
The Modal interval is 30-40, L = 30, i = 10
f0 = 20, f1 = 43, f2
= 32
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