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MODE

Mode is the value of a variable which occurs most frequently in a set of observations.

For simple frequency distribution the mode is the value of a variable corresponding to the maximum frequency. For grouped frequency distribution the mode is obtained as follows.

where,

L = Lower limit or boundary of the modal class

= Width of the modal class

f1= Frequency of the modal class

f 0= Frequency of the class preceding the modal class

f2 = Frequency of the class succeeding the modal class.

Note. 1. If  2f1- f0 -f2 = 0, then the mode is obtained as follows :

2. lf the maximum frequency is repeated then the above technique is not practicable.

3. For symmetrical distribution,

Mean = Median = Mode. (Mean = x).

However, for moderately skewed distribution there is an empirical relationship due to Karl Pearson i.e.,

Mean - Mode = 3 (Mean - Median).

 

Example 5 : Find the mode of the problem as given in example 4. 

Solution. Here maximum frequency is 25, so the modal class is 61-70.

L = 61,  = 9,  f1 = 25,  f0 = 15, f2 = 10