text: 1
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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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explanation: The document contains a math question and its solution. The question is about finding the common difference (d) of an arithmetic progression (A.P.) given the standard deviation of four consecutive numbers in the A.P. The correct answer is provided as ±2.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 1
  You visited us 1 times! Enjoying our articles? Unlock Full Access!
  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
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  B
  
  ±25
  
  No worries! We‘ve got your back. Try BYJU‘S free classes today!
  C
  ±2
  Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
  D
  ±2
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  Open in App
  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
  
  Suggest Corrections
  0
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  Related Videos
  Practice Set 1
  MATHEMATICS
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its solution. The question is about finding the common difference (d) of an arithmetic progression (A.P.) given the standard deviation of four consecutive numbers in the A.P. The correct answer is provided as ±2.
  
  Label: question-and-answer