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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Practice Set 1
MATHEMATICS
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The text contains a multiple-choice question about the common difference of an arithmetic progression (A.P.) with a provided solution.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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

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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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Practice Set 1
MATHEMATICS
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user
The text contains a multiple-choice question about the common difference of an arithmetic progression (A.P.) with a provided solution.

TYPE: SINGLE_QUESTION_WITH_ANSWER