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Average

 Average or Mean = Description: 764.png

Variance and standard deviation

  • The variance of a variate X is the arithmetic mean of the squares of all deviations of X from the arithmetic mean of the observations and is denoted by Var (X) or σ2
  • The positive square root of the variance of a variate X is known as standard deviation. i.e., Description: 769.png
  • To calculate the sum of quantities, they should be in the same unit.
  • Average of a group consisting two different groups when their averages are known:
     
    Let Group A contains m quantities and their average is a and Group B contains n quantities and their average is b, then average of group C containing a + b quantities Description: 774.png 
  • If, in a group, one or more new quantities are added or excluded, then the new quantity or sum of added or excluded quantities = [Change in no. of quantities × original average] ± [change in average × final no. of quantities]
     
    Take +ve sign if quantities added and take –ve sign if quantities removed.




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