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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



Your Answer
A

±5

Your Answer
B

±25

Correct Answer
C

±2
 

Your Answer
D

±2


Solution

The correct option is C

±2
 


Let 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=52.25 d2+0.25 d2+0.25 d2+2.25 d2=5×45 d2=20d2=4d=±2

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