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Find the positive value of x if the standard deviation of the numbers 1, x…

Find the positive value of x if the standard deviation of the numbers 1, x + 1 is 6
  • A.
    1
  • B.
    2
  • C.
    3
  • D.
    4
Correct Answer: Option C
Explanation

mean (x) = (frac{1 + x + 1 + 2x + 1}{3})
= (frac{3x + 3}{3})
= 1 + x
(begin{array}{c|c} X & (X -X) & (X -X)^2\ hline 1 & -x & x^2 \ x + 1 & 0 & 0\2x + 1 & x & x^2\ hline & & 2x^2end{array})
S.D = (sqrt{frac{sum(x – 7)^2}{sum f}})
= (sqrt{(6)}^2)
= (frac{2x^2}{3})
= 2x2
= 18
x2 = 9
∴ x = (pm) (sqrt{9})
= (pm)3

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