☼ Results  On  Mode  :

 (i) Ungrouped  Data : –

  Z    =    The observation which is repeated for maximum number of times.

 (ii) Discrete Data ( Grouped Data ) : –

  Z   =   The observation against maximum Frequency.

 (iii) Continuous Data ( Grouped  Data )  : –

              First arrange all the Classes of Frequency Distribution in ascending order and also convert all the class in exclusive Class Interval if they are inclusive Class Interval

  Now,   Modal  Class   =   The Class having Maximum Frequency

  Now,   Z  =

                            Where, L = Lower limit of   Modal Class.

   f_m = The  Frequency  of the Modal Class

   f₁ = Frequency of  the class preceding the Modal Class.

   f₂ = Frequency of  the class succeeding the Modal Class.

   C = Class – Length of  the Modal Class.

 Note  If  there is no any observation which repeat maximum times or all the observation appear in the data exactly once, then the given data has not any Mode. Or Mode for the given data does not exist.

    If there are two observations which repeat maximum times, then those both observations are called Mode. And the data is called Bi–Modal Data.

    If  there are more than two such observations, then those all observations are called Mode and the data is called Multi-Modal Data.

    If  the frequency Distribution  is  Bi-Modal  or  of  Unequal Class–Length,  then  only we can use the following  formula :

Z  =  3 M  –  2

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