Mode in statistics | How to calculate the mode | Mode formula.

Mode in statistics :

Mode definition :

For example, some data such as follows :
2, 1, 2, 5, 4, 2, 2, 7, 8, 2.
Here, 2 value repeated 5 times that is repeated many times as compared another data. Therefore, 2 is Mode."

It is straight forward to calculate mode in case of individual and discrete data.

             Mean        Median        Quartile

How do you find the mode of Individual Data ?

Que. 1) The following are the marks of 10 students. Calculate the mode.

60, 67, 76, 56, 77, 67, 48, 67, 89, 90.

Ans. :

Marks           : 48  56  60  67  76  77  89  90
Frequency  :  01  01  01  03  01  01  01  01
Here 67 mark repeated many times that is 3 times.

therefore, Mode = 67.

Que. 2) The following are the height in cm of 12 students. Calculate the mode.
40, 41, 43, 41, 46, 47, 41, 41, 40, 42, 41,  46.
Ans. :
Heights        : 40  41  42  46  47
Frequency  :  02  05  01  03  01
Here 41 cm  height repeated many times that is 5 times.
therefore, Mode = 41.

How do you find the mode of discrete data?
Que. 1) Calculate the mode from the following data.
x : 15   20   25   30   35   40
f : 10    12   56   32   08   06
Ans. :
Here maximum frequency 56 corresponds to value 25. hence, Mode = 25.

Que. 2) Calculate the mode from the following data.
age ( x )                               : 25    26    27    28   29    30    31
number of persons ( f )        : 04    06   17    75    21    62   02
Ans. :
Here maximum frequency 75 corresponds to value 28. hence, Mode = 28.

How do you find the mode of continues data?
For calculate of mode in case of continues frequency distribution following rules are to be follow.
Rule 1 : Find modal class. Modal class is the class having maximum frequency.
Rule 2 : Formula,
Mo = L1 + [ ( f1 - f0 ) / ( 2f1 - f0 - f2) ] × i
Where, 
L1 = the lower limit of the modal class,
f1 = frequency of the modal class,
f0 = frequency of the previous class,
f2 = frequency of the next class,
i = class interval of the modal class.

Que. 1) Calculate mode of the following distribution showing x - Wages in Rs. and f - No. of workers.
x : 70-80, 80-90, 90-100, 100-110
f :       7           10         15             6         
Ans. :
Here the maximum frequency is 15, therefore modal class = 90 - 100.
f1  = 15
f0 = 10
f2 = 06
i = 10
L1 = 90
Mo = L1 + [ ( f1 - f0 ) / ( 2f1 - f0 - f2) ] × i
Mo = 90 + [ ( 15 - 10 ) / ( 30 - 10 - 6 ) ] × 10
Mo = 90 + ( 5 / 14 ) × 10
      = 90 + 0. 3571 × 10
       = 90 + 3. 5714
       = 93.5714
      = 93.57
therefore, Mode = Rs. 93.57

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