Continuous Series Data
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In which entire available data is divided into equal intervals. Each group represents different values but with same range. Formulas for calculating Arithmetic mean
Direct Method:
Shortcut method without step deviation:
Shortcut method with step deviation:
In continuous series x is middle value for each class. x =
where is lower limit and is upper limit.
And C is Class interval.
Example: Find out Arithmetic mean for the given data.
x (marks) 







F (no. of students) 







Direct Method:
Class interval  x =  f  fx 




























= 300 

.
Shortcut Method:
Without Step deviation:
Class interval  x =  f  dx = xA  fdx 



































= 300 

With Step deviation:
Class interval  x =  f  dx = xA  dx’ = dx/C  fdx’ 












































Precautions of Using Arithmetic Mean:

Arithmetic Mean is a theoretical value which may not represent actual fact.
Ex: Average children per family would be 2.3 but it is unrealistic. There would be either 2 children or 3 children per family. Note: There is a possibility for no children in some families.

Arithmetic Mean cannot be calculated for qualitative data such as honesty, beauty etc.