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Mode:                                                                                                                                      Bookmark and Share
 
 

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:

  1. Arrange the series in ascending or descending order
  2. Find the term which is occurring most of the times. This term is Mode (Z).

To find the Mode in a series

10

8

7

4

10

5

12

7

10

11

Arranging the series in ascending order

4

5

7

7

8

10

10

10

11

12

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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