text: ## What is Calculation Of Mean?
  
  Example:
  The following data relate to the age of a group of Govt. employees. Calculate the arithmetic mean and standard deviation:
  
  Age                    50—55      45—50     40—45       35-40    30—35        25—30     20—25
  
  No. of                  25                30            40            45            80          110          170
  
  Employees.
  
  Solution: Calculation of Mean and S.D. by step-deviation method
  
   Age Mid- No. of Dev. From Step Devia- (X) (mv) (f) Dx dx2 Fdx fdx2 S0-5S 52.5 25 15 +3 9 +75 225 45—50 47.5 30 +10 +2 +60 120 40-45 42.5 40 +5 +1 +40 40 35—40 37.5 45 0 0 +0 0 30—35 32.5 80 — 5 —1 —80 80 25—30 27.5 110 —10 —2 —220 440 20-25 22.5 170 —15 —3 —510 1530 ∑f = 500 ∑fdx = -635 ∑fdx2 = 2435
  
  Arithmetic Mean or X = A + (∑fdx)/N) × i  = 37.5 + (-635)/500 × 5 = 31.15 years
  
  Standard-Deviation σ = √(∑fdX2))/N- ((∑fdx)/N  )2 ) × i  =  √(2435/500- ((-635)/500 )2 ) × 5
  
  = √(3.27 )×5
  
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