Maths Class 10 Chapter 14: Statistics

Important Formulas

        1.      The mean for grouped data can be found by the following methods:

          i.            Direct method: In direct method, we use the following formula:                                 

         

    ii.            Assumed mean method: In assumed mean method, we use the following formula:

                                 

       iii.            Step deviation method: In this method, we use the following formula:

                                  

        2.      The mode for grouped data can be found by the following formula:

                   

where l = lower limit of modal class

           h = size of the class interval

           f₁ = frequency of the modal class

           f₀ = frequency of the class preceding the modal class

           f₂ = frequency of the class succeeding the modal class

  
        3.      The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.

        4.      The median for grouped data is found by the following formula:

                                                       

where l = lower limit of median class

           n = number of observations

           cf = cumulative frequency of class preceding the median class

           f = frequency of median class

           h = class size

      5.      We can represent a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the less than type and of the more than type.

      6.      The median of grouped data can be obtained graphically as the x-coordinate of the point of intersection of the two ogives, e.g., intersection of less than type and more than type ogive.