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  Question
  
  # The standard deviation of 4 consecutive numbers which are in A.P is √5. The common difference (d) of this A.P is
  
  A
  
  ±5
  
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  B
  
  ±25
  
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  C
  ±2
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  D
  ±2
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  Solution
  
  ## The correct option is C ±2Let the four numbers be a, a+d, a+2d and a+3d Mean, ¯x=a+(a+d)+(a+2d)+(a+3d)4=a+1.5dσ=√∑(xi−¯x)24=√(−1.5d)2+(−0.5d)2+(0.5d)2+(1.5d)24=√5⇒2.25 d2+0.25 d2+0.25 d2+2.25 d2=5×4⇒5 d2=20⇒d2=4⇒d=±2
  
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